Question 1

Which equation correctly represents the elastic potential energy stored in a spring that is stretched or compressed by a distance $$x$$ from its equilibrium position?

Accepted Answer

$$U_{sp} = \frac{1}{2}kx^2$

Question 2

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and pulled a distance $$A$$ from equilibrium, then released from rest. What is the speed of the block as it passes through the equilibrium position?

Accepted Answer

$$v = \sqrt{\frac{k}{m}}A$$

Question 3

If a spring is compressed by $$x_0$$ and then released, what is the total mechanical energy of the system, assuming no energy is lost?

Accepted Answer

$$E = \frac{1}{2}kx_0$^2$$

Question 4

Which of the following best describes the energy exchange in a simple harmonic oscillator (such as a mass-spring system)?

Accepted Answer

Potential energy and kinetic energy trade off, with their sum remaining constant.

Question 5

A pendulum swings back and forth. At its highest point, which statement about its energy is correct?

Accepted Answer

Potential energy is maximum, kinetic energy is zero.

Question 6

For a spring with spring constant $$k$$, what is the force required to stretch the spring by a distance $$x$$?

Accepted Answer

$$F = kx$$

Question 7

A block attached to a spring is released from rest at $$x = A. $$What is its kinetic energy when it passes through $$x = 0$$?

Accepted Answer

$$K = \frac{1}{2}kA^2$

Question 8

If the spring constant $$k is $$doubled, how does the elastic potential energy stored in the spring change for the same displacement $$x$$?

Accepted Answer

It is multiplied by 2.

Question 9

Which graph best represents the relationship between elastic potential energy and displacement for a spring?

Accepted Answer

A parabola opening upwards.

Question 10

A block of mass $$m is $$attached to a spring and oscillates with amplitude $$A. $$What is the maximum acceleration experienced by the block?

Accepted Answer

$$a_{max} = \frac{kA}{m}$$

Question 11

At what position is the kinetic energy of a mass-spring oscillator zero?

Accepted Answer

At the maximum displacement ($$x = \pm A).$$

Question 12

A pendulum of length $$L$$ and mass $$m$$ swings with amplitude $$\$$theta_0$$. What is the maximum potential energy relative to the lowest point?

Accepted Answer

$$U_{max} = mgL(1 - \cos \$$theta_0$$)$$

Question 13

If a spring is stretched twice as far from equilibrium, how does its elastic potential energy change?

Accepted Answer

It quadruples.

Question 14

Which of the following is true about the total mechanical energy in an ideal mass-spring system?

Accepted Answer

It remains constant.

Question 15

A block attached to a spring is released from $$x = A$$ with zero initial velocity. At $$x = \frac{A}{2}$$, what is its kinetic energy?

Accepted Answer

$$K = \frac{3}{8}kA^2$

Question 16

Which of the following statements about energy in a pendulum is correct?

Accepted Answer

Kinetic energy is maximum at the lowest point.

Question 17

A spring with spring constant $$k is $$compressed by $$x. If $$the block attached to the spring is released, what is its speed when the spring returns to equilibrium?

Accepted Answer

$$v = \sqrt{\frac{k}{m}}x$$

Question 18

Which of the following best describes the phase relationship between kinetic and potential energy in a simple harmonic oscillator?

Accepted Answer

When one is maximum, the other is minimum.

Question 19

A block of mass $$m is $$attached to a spring and oscillates with amplitude $$A. $$What is the total energy of the system?

Accepted Answer

$$E = \frac{1}{2}kA^2$

Question 20

If the mass of a block attached to a spring is doubled, how does the maximum speed at equilibrium change (for the same amplitude $$A$$)?

Accepted Answer

It decreases by a factor of $$\sqrt{2}.$$

week 7 handout

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