Consider a spring-mass system given by mu" + yu' + ku = 0. a. Suppose y² > 4mk and the initial conditions are u(0) = 5, u'(0) = a HUGE negative number. How many time(s) will the mass pass through the equilibrium position? JUST GIVE ME A NUMBER AS YOUR ANSWER. Infinity is considered a number. b. Same as above with y² = 4mk and u(0) = 2, u'(0) = a HUGE positive number . Infinity is considered a number. C. Suppose <4mk and the initial conditions are u(0) = -.0001, u'(0) = 0. How many time(s) will the mass pass through the equilibrium position? JUST GIVE ME A NUMBER AS YOUR ANSWER. Infinity is considered a number. d. If y = 2 what is the limit of u(t) as t→∞? JUST GIVE ME A NUMBER AS YOUR ANSWER. Infinity is considered a number.

5. A 60 kg circus performer is swinging from a trapeze bar.A: She is 10 m off the ground with a speed v1. The spring-board platform below her is atits equilibrium length.B: She lets go of the trapeze bar and lands on th spring-board platform, which compresseswhen she lands on it. When she is stationary, she is 2 m off the ground and the springis maximally compressed.C: The spring-board extends and launches her back into the air. As soon as the spring istotally relaxed again, the performer is 3 m off the ground and has a speed v2.D: The performer lands on a platform 10 m above the floor, and she stands stationary. a. Her initial speed v1 = 10 m/s. What is her total energy at point A?  b. Between points A and B, assume none of her energy is lost to heat or friction. Whenshe is stationary on the compressed platform at B, how much energy is stored in thespring-board platform?  c. When the spring-board platform is fully released at point C, what must her speed v2 be?

A spring with a spring constant of 100 N/m is stretched by a force of 10 N. What is the elastic PE stored in the stretched spring? a. 0.5J b. 0.3J C. 0.4J d. 0.25 J

1. What can you say about the relationships of mass, spring constant, and spring compression to the velocity of the body? 2. Work done on a system puts energy into it. Work done by a system removes energy from it. How will you relate this to energy transformation? 3. Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independents of the direction thrown. (Hint: show that K0 + U0 = Kf + Uf )

4. Suppose a block of mass m slides over a surface with kinetic friction coef- ficient towards a spring with spring constant k. The block reaches the spring with spring with speed vo. (a) How far is the spring compressed at maximum compression? Give your answer in terms of m, k, lk, and vo. (b) What is an expression for the maximum value that v。 could be in order for the spring to remain maximally compressed, no matter what material the block and surface are? Give your answer in terms of m, k, pk. Hint: the coefficient of static friction is always greater than the coefficient of kinetic friction.

43. A 200 g mass stretches a spring 40 cm. How much Potential energy does the spring have?A. .392 JB. 1.236 JC. .983 JD. .677 J

8. A model car of mass 4.5 kg slides down a frictionless ramp into a spring constant k=4.85kN/m. a. The spring experiences a maximum compression of 21 cm. Determine the height of the initial release point. b. Calculate the speed of the model car when the spring has been compressed 12 cm. hc. Determine the maximum acceleration of the car after it hits the spring.

3. A block of mass m=1.2 kg is attached to a horizontal spring of force constant k=75 N/m. The block is pushed, and spring is compressed, to the position 10.0 cm to the left of the equilibrium position; then, block is released. A. Neglect friction. Find the speed of the block as it passes through the equilibrium position. B. If the friction is significant and µ = 0.22, what is the speed of the block as it passes through the equilibrium position?

1. A block of mass m is pushed against (but not attached to) a spring with stiffness k so that the spring is compressed a distance Ar. When released, the block slides across the frictionless surface of a shelf a height h above the floor, the then falls to the floor. a. What is the speed of the block at the moment it leaves the shelf? V2 = b. What is the speed of the block at the moment just before it hits the ground? Vr =

Fs = kx 6000 N= 400 N/m x = 15 cm 6.In a spring experiment the results were as follows: Force (N) 1 4 5 7 Length (mm) 50 58 70 74 82 90 102 125 Extension (mm) 8 20 24 32 40 52 75 a. What is the length of the spring when unstretched? b. Complete the 'Extension' row of the table C. Plot a graph of extension against force. Circle the anomalous point. d. Mark the limit of proportionality on your graph (elastic limit). е. What load would give an extension of 30mm? f. What would be the spring length for a load of 4.5N? g. Extension: Determine a value for the spring constant in this example. DELL