4 . A mass on a spring has a frequency of 2.5 Hz and an amplitude of 0.05 m. In one complete period,
what distance does the mass traverse? (This question asks for the actual distance, not the
displacement.)
(A) 0.05 cm
(B) 0.01 cm
(C) 20 cm
(D) 10 cm
(E) 5 cm
5 . Increasing which of the following will increase the period of a simple pendulum?
I. the length of the string
II. the local gravitational field
III. the mass attached to the string
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Free Response:
6 . A mass m is attached to a horizontal spring of spring constant k . The spring oscillates in simple
harmonic motion with amplitude A . Answer the following in terms of A .
(a) At what displacement from equilibrium is the speed half of the maximum value?
(b) At what displacement from equilibrium is the potential energy half of the maximum value?
(c) When is the mass farther from its equilibrium position, when its speed is half maximum, or when
its potential energy is half maximum?
Solutions to Practice Problems
1 . The ball is not in simple harmonic motion. An object in SHM experiences a force that pushes toward
the center of the motion, pushing harder the farther the object is from the center; and, an object in SHM
oscillates smoothly with a sinusoidal position–time graph. The basketball experiences only the
gravitational force, except for the brief time that it’s in contact with the ground. Its position–time graph
has sharp peaks when it hits the ground.
2 . B— The period of a pendulum is
All that is changed by going to Jupiter is g , which is multiplied by 3. g is in the denominator and
under a square root, so the period on Jupiter will be reduced by a factor of . So the original 5-
second period is cut by a bit less than half, to about 3 seconds.
