A Spring with a Hooke's law constant of K N/m and an unstretched length of 1 cm is hung vertically from a support. A block is attached to the free end of the spring and let go from rest; the lowest point reached by the mass is Y cm from the support attachment Use g = 10 m/s/s K= 32 NIM I Lum L= 22 cm Y= 38 cm Determine the following: 1) the amplitude of vibration 2) the mass of the block 3.) the period and counting frequency of vibration 4.) the maximum speed of the block while vibrating Y cm

Principles of Physics: A Calculus-Based Text
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Chapter12: Oscillatory Motion
Section: Chapter Questions
Problem 54P
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Please start each question with one of the equations provided.
A Spring with a Hooke's law constant of K N/M
and an unstretched length of L cm is hung vertically
from a support. A block is attached to the free end
of the spring and let go from rest; the lowest
point reached by the mass is Y cm from the support
attachment Use g = 10 m/s/s
K= 32 NIM
I Lum
L= 22 cm
Y= 38 cm
Determine the following:
1) the amplitude of vibration
2) the mass of the block
3.) the period and counting frequency of vibration
4.) the maximum speed of the block while vibrating
y cm
*The first step for each answer be one of the
equations below:
9-10 m/s/s
HOOKE's Law: F=-Kx
Period, Frequency: w 2π f = 2π/T
Natural frequency of a system: w = √
The simple pendulum : T = 2T₁
T√
Vibrational equations of motion:
x (t) = A cos (wt + 4)
v (t)=-Aw sin (wt + (p)
a(t)= Awa (os (wt + 4)
Transcribed Image Text:A Spring with a Hooke's law constant of K N/M and an unstretched length of L cm is hung vertically from a support. A block is attached to the free end of the spring and let go from rest; the lowest point reached by the mass is Y cm from the support attachment Use g = 10 m/s/s K= 32 NIM I Lum L= 22 cm Y= 38 cm Determine the following: 1) the amplitude of vibration 2) the mass of the block 3.) the period and counting frequency of vibration 4.) the maximum speed of the block while vibrating y cm *The first step for each answer be one of the equations below: 9-10 m/s/s HOOKE's Law: F=-Kx Period, Frequency: w 2π f = 2π/T Natural frequency of a system: w = √ The simple pendulum : T = 2T₁ T√ Vibrational equations of motion: x (t) = A cos (wt + 4) v (t)=-Aw sin (wt + (p) a(t)= Awa (os (wt + 4)
Hooke's Law:
Period, frequency:
Natural frequency of a system:
The simple pendulum:
Vibrational equations of motion:
x(t) = A cos(@t + p)
F = -kx
wwwwww
@ = 2n f = 2n/T
√
√
W3
T = 2π
v(t) = -Aw sin(wt + p)
a(t) = Aw² cos(wt + p)
Transcribed Image Text:Hooke's Law: Period, frequency: Natural frequency of a system: The simple pendulum: Vibrational equations of motion: x(t) = A cos(@t + p) F = -kx wwwwww @ = 2n f = 2n/T √ √ W3 T = 2π v(t) = -Aw sin(wt + p) a(t) = Aw² cos(wt + p)
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