Question

An oscillating block-spring system has a mechanical energy of 2.38 J, an amplitude of 7.65 cm, and a maximum speed of 3.26 m/s. Find (a) the spring constant, (b) the mass of the block and (c) the frequency of oscillation.

Answer 1

Mechanical energy of the oscillating system = E = 2.38 J

Amplitude = A = 7.65 cm = 0.0765 m

Maximum speed = V_max = 3.26 m/s

Spring constant = k

Mass of the block = m

Frequency of oscillation = f

Angular frequency of oscillation =

Mechanical energy of the system is equal to the maximum potential energy of the spring.

E = kA²/2

2.38 = k(0.0765)²/2

k = 813.36 N/m

V_max = A

3.26 = (0.0765)

= 42.614 rad/s

m = 0.448 kg

f = 6.782 Hz

a) Spring constant = 813.36 N/m

b) Mass of the block = 0.448 kg

c) Frequency of oscillation = 6.782 Hz