A particle is moving in a straight line with simple harmonic motion. Its velocity has the values of 5 and 4 m/s when its distances from the center point of its motion are 2 and 3 m, respectively. Find the length of the path and the frequency of oscillation.

A particle is moving in a straight line with simple harmonic motion. Its velocity has the values of 5 and 4 m/s when its distances from the center point of its motion are 2 and 3 m, respectively. Find the length of the path and the frequency of oscillation.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: A mass of 4 kg is suspended from a spring and oscillates up and down at 2 Hz. Determine the…

Q: Express, as a function of t, the time interval needed for the amplitude of an oscillation to reduce…

A: As the amplitude of an oscillation is reducing, it has to be damped oscillation. In damped…

Q: 1. Consider two pendulums, 1 and 2, with the same string length L, but with different bob masses m1…

A: As per our guidelines we are supposed to answering only one question. Kindly repost other questions…

Q: A hockey puck oscillates on a frictionless, horizontal track while attached to a horizontal spring.…

Q: Two masses, m and M, are connected by a spring whose force constant is k and slide freely on a…

A: given; two mass m &Mspring constant=knatura frequency of occilation(ω)=?

Q: A toy battery-powered plane is hanging from the ceiling. With the motor turned off it is pulled to…

Q: Find the natural frequency of the system for small oscillations.

A: Given: To determine: Natural frequency for small oscillation

Q: 3. An undamped spring-mass system has a mass that weighs 48 lb and a spring constant 0.5 lb/in. The…

A: This question is related to the spring-mass system. The elastic vibration wherever there's no…

Q: Determine the natural frequency of the system shown beside using Motion equation

Q: Suppose that an object attached to a coiled spring is pulled down a distance of 10 inches from its…

Q: The masses m1 and m2, connected by an elastic cord, move in the vertical direction with small…

Q: 2) A block of mass m is attached to a spring with force constant, k and oscillate at a frequency f.…

A: The initial frequency of the spring-mass system is given as, f=12πkm Here, k, and m represent spring…

Q: Consider a place where the gravity is one-fourth the gravity on Earth (g' = g/4), then the frequency…

A: Given data: The gravity on the earth is g The gravity on the other place is g'=g4 The frequency of…

Q: A diving board oscillates with simple harmonic motion of frequency 2.5 cycles per second. What is…

Q: In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max,…

A: Given: θmax"θmax'= 2π s-1 For an oscillatory motion of the simple pendulum, Velocity is given by,…

Q: Explain Simple Harmonic Motion. Obtain expression for the frequency , amplitude velocity , and…

A: Simple harmonic motion (SHM) – It is stated as a motion in which the restoring force is directly…

Q: It is impossible for two particles, each executing simple harmonic motion, to remain in phase with…

A: Option b is correct.

Q: In the shown figure, let m1 = 1 kg, m2 = 2 kg, kı = k3 = 100 N/m and k2 = 200 N/m. (a) Write the…

A: Consider a mass-spring system having two masses attached with three spring in the longitudinal…

Q: 03 the mass of a spring-mass-dashpot system is given an initial velocity 10W,, where 10W„is the…

A: As it contains multiple questions. I am answering only one question (3) . So, post the question…

Q: Determine the period of small oscillations of a small particle that moves without friction inside a…

Q: In the shown figure, let mị = 1 kg, m2 = 2 kg, k1 = k3 = 100 N/m and k2 = 200 N/m. (a) Write the…

A: The above question is related to spring mass system.

Q: In the shown figure, let m1 = 1 kg, m2 = 2 kg, ki = k3 = 100 N/m and k2 = 200 N/m. (a) Write the…

A: Question (A) & (B) are solved here. For Question (C), Please post this question again.

Q: Simple harmonic motion has a amplitude of 0.3 cm and a period of 0.2 seconds. Determine the maximum…

Q: (a) A mass suspended from a helical spring of stiffness s, is displaced by a distance x from its…

Q: Consider a place where the gravity is one-fourth the gravity on Earth (g' = g/4), then the frequency…

A: Given data g' = g/4

Q: 2. The amplitude of simple harmonic motion is 600 mm, and the period is 1 s. Determine the maximum…

A: Calculated maximum velocity and acceleration.

Q: A simple pendulum is subjected to an initial excitation and oscillates in a frequency of 0.8 Hz. If…

A: Frequency of oscillation of the simple pendulum F=0.8Hz The time period of oscillation of the simple…

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

A: Given : Amplitude, A = 0.1 m In Simple Harmonic Motion, The motion of the mass-spring system…

Q: Task 2 In the shown figure, let m1 = 1 kg, m2 = 2 kg, k = k3 = 100 N/m and k2 = 200 N/m. (a) Write…

A: The above question is related to spring mass system.

Q: A mass of 25 kg is suspended on a spring and set oscillating . A dashpot is fitted between the mass…

Q: A simple harmonic motion as shown in Figure Q1(a) has a maximum velocity of (P+1) m/s with (Q+2)…

A: Given data: matrix num (ad200107) Vmax=P+1 m/sVmax=1=1=2m/sT=Q+2 sT=2 sx0=R+1 mmx0=7+1=8mm

Q: A mass-spring system oscillates on a frictionless horizontal surface in simple harmonic motion with…

Q: n object of mass 2 kg is attached to a spring of stiffness 200 N / m on a horizontal frictionless…

A: Frequency is given by,ω=kmω=2002ω=10 radian/s

Q: Find the natural frequency of the following system. Ignore the mass of the pulleys. k k m

A: Natural Frequency: The frequency at which system vibrates or oscillates when not subjected to…

Q: Q2: For a system the equations of motion are as shown below, find frequencies and mode shapes. Ţ…

Q: The equations of motion of a two – degree – of freedom system are given as follows. [3k k Determine…

A: The natural frequency is calculated as: mω2-K=0det2m004mω2-3kkk4k=0for,m=5 kgk=100…

Q: A block of mass m is attached to a spring with force constant k and oscillate at a frequency f. If…

Q: A spring oscillates with simple harmonic motion at a frequency of 6.33 Hz when a mass of 3.22 kg is…

A: A type of periodic motion in which restoring force is directly proportional to the displacement of…

Q: A simple pendulum is set into oscillation from Its rest position by giving it an angular velocity of…

A: Write the equation of motion of the given system. Here, m represents the mass, θ represents the…

Q: Figure TQ3.5 shows a simple pendulum of length lh has a bob of mass m1. Another simple pendulum of…

A: Write the given expression. ω4g2-l1+l2l1l2m1+m2m1ω2g+m1+m2m1l1l2=0 Write the given data. m1=1…

Q: A light ball of mass m is tightly stretched by strings with initial tension, T, as shown in the…

A: Given data: Mass = m Tension = T Need to natural frequency.

Q: A mass m oscillates on a spring with spring constant k, with amplitude d. At the moment when the…

A: Before collision ,When the block is at a position,x=d2 there is only mass m, assuming velocity of…

Q: A horizontal spring mass system with Coulomb damping has a mass of 5 kg attached to a spring of…

Q: A body of mass 18 kg moves with simple harmonic motion. When it is 0.24 mm from mid-point, it has…

Q: Consider a place where the gravity is one-fourth the gravity on Earth (g' = g/4), then the frequency…

Q: A block-spring system oscillates in a simple harmonic motion on a frictionless horizontal table. Its…

Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

VIBRATION ENGINEERING

Solve the following problem. Show complete solutions.

View Image

6. A particle is moving in a straight line with simple harmonic motion. Its velocity has the values of
5 and 4 m/s when its distances from the center point of its motion are 2 and 3 m, respectively.
Find the length of the path and the frequency of oscillation.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

On an alien planet, a simple pendulum of length 0.300 m has oscillation frequency 0.609 Hz. Find the period of the pendulum. Find the acceleration due to gravity on this planet's surface.
3. An undamped spring-mass system has a mass that weighs 48 lb and a spring constant 0.5 lb/in. The mass is suddenly set in motion at t = 0 by an external force of 3 cos(2t) lb. Assume that the gravitational acceleration is g = 32 ft/s?. What is the natural frequency for this spring-mass system? Find the position of mass as a function of time t.
The figure represents a front wheel-drive vehicle with a total mass of 1650 kg. Analyze the equilibrium of forces and moments and answer the questions. 620mm 1.8m 1.2m Fig. Front-Wheel-Drive The normal reactions on both set of wheels when the vehicle is at rest on a horizontal road surface are: Nfo = N on front wheels and Nro = N on rear wheels Analyze, with the a proper force diagram and make your determination: the vehicle needs to at a rate of mls2 to achieve equal equal normal forces on both set of rear and front wheel. During the sudden change of speed (acceleration or deceleration, depending on the results informed by your calculation), reactions are respectively N1 = N on rear wheels and NI = N on front wheels. If the same front-wheel-drive vehicle is driven so as to maintain a constant speed up a gradient of 14%, the normal reactions on the the wheel as the vehicle moves up the incline, are respectively, N, = N on rear wheels and Nf. N on front wheels resulting into %3D ratios…
A harmonic motion has a frequency of 30 cycle/second and its maximum velocity is 10 m/s. Determine its Amplitude, Period and maximum acceleration.
A simple pendulum is subjected to an initial excitation and oscillates in a frequency of 0.8 Hz. If the length of the pendulum is increased by 50%, find the new period of oscillation (in .sec)
A tuning fork is struck, producing a pure tone as its tines vibrate. The vibrations are modeled by the function v(t) = 0.7 sin(880t) where v(t) is the displacement of the tines in millimeters at time t seconds. Find the period of the vibration.
Find the amplitude, frequency and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is x=(0.250m) cos(π800t) a. Find the maximum magnitude of the velocity and acceleration. b. What is the position, velocity and acceleration of the object after 100s has elapsed?
Each piston of an engine makes a sharp sound every other revolution of the engine. How fast is a race car going if its eight-cylinder engine emits a sound of frequency 750 Hz, given that the engine makes 2000 revolutions per kilometer? At how many revolutions per minute is the engine rotating?
3. A particle of mass 20 g is connected to one end of a spring on a frictionless horizontal surface and moving in a simple harmonic motion about the origin. The displacement given by x = 2 sin 3t , where x is in meters and time, t is in seconds. The motion starts when t = 0. (a) , What is the total distance travelled by the particle at time t = 3T/4, where T is the time period? (b) Find the kinetic and potential energy of the particle at time t = 3T/4. * What is the acceleration of the particle when it first comes to a rest? (c) t
Determine the natural frequency of the system shown beside using Motion equation
The acceleration in simple harmonic motion is maximum when its velocity is a. Zero
A mass hanging from a vertical spring and a simple pendulum each have a period of oscillation of 1 second on the earth. If you were to take these devices to another planet where the acceleration due to gravity is greater than on earth, state whether the period of each device is greater than 1 sec, less than 1 sec, or the same. Explain your reasoning.