Part A = A

Part B = A

Part C = moving toward equilibrium.

Part D = C

Part E = C

Part F = D

Part G = 3/8kA^{2}

Consider a harmonic oscillator at four different moments, labeled A, B, C, and D, as shown in the figure . Assume that the force constant k, the mass of the block, m, and the amplitude of vibrations, A, are given. Which moment corresponds to the maximum potential energy of the system?

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Part A = 0.34m

Part B = 0.29m (watch out though, see the solutions below for details)

A 2.5 kg box that is sliding on a frictionless surface with a speed of 10 m/s approaches a horizontal spring.

If one end of the spring is fixed and the other end changes its position, how far will the spring be compressed in stopping the box?

How far will the spring be compressed when the box’s speed is reduced to half of its initial speed?

A horizontal spring, resting on a frictionless tabletop, is stretched 18 cm from its unstretched configuration and a 1.00kg mass is attached to it.

How does its final potential energy compare to its initial potential energy?

A particular spring has a force constant of 1.5×103 N/m. How much work is done in stretching the relaxed spring by 5.0 cm? How much more work is done in stretching the spring an additional 3.0 cm?

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Part A =

- Mechanical energy is conserved because no dissipative forces perform work on the ball.
- The forces of gravity and the spring have potential energies associated with them.

Part B = 4.78m/s

Part C = 1.17m

Part D =

- increasing the spring constant k
- increasing the distance the spring is compressed
- decreasing the mass of the ball

Fun with a spring gun mastering physics: A spring-loaded toy gun is used to shoot a ball of mass m = 1.50kg straight up in the air, as shown in the figure.

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Part A = From x = 2d to x = 3d

Part B = The same amount of energy is required to either stretch or compress the spring.

Part C = Spring A must stretch half the distance spring B stretches.

Part D = Spring A requires the same amount of energy as spring B.

As illustrated in the figure, a spring with spring constant k is stretched from x = 0 to x = 3d, where x = 0 is the equilibrium position of the spring. During which interval is the largest amount of energy required to stretch the spring?

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