Question

1. An object is vibrating in SHM with an amplitude of 12.0 cm and a frequency of 4 Hz. What is the minimum and maximum acceleration? (Use x = 0 at equlibrium and + to the right).
A. 0, ±76 m/s2
B. 0, ±39 m/s2
C. ±4, ±18 m/s2
D. ±4, ±81 m/s2

2. For the object in the previous question, what is the speed when x = 5.0 cm?
A. 1.33 m/s
B. 9.80 m/s
C. 8.71 m/s
D. 2.74 m/s

Answer 1

Question 1

Amplitude = A = 12 cm = 0.12 m

Frequency = f = 4 Hz

Angular frequency =

= 2f

= 2(4)

= 25.13 s^-1

Maximum magnitude of acceleration = a_max

a_max = A²

a_max = (0.12)(25.13²)

a_max = 75.79 m/s²

Rounding off,

a_max = 76 m/s²

At the left end it will have an acceleration of +76 m/s² and at the right end it will have an acceleration of -76 m/s².

Option A is correct.

Question 2

x = 5 cm = 0.05 m

Velocity at any instant = V

V = 2.74 m/s

Option D is correct.