Question

An oscillating block-spring system has a mechanical energy of 0.872 J, an amplitude of 10.7 cm, and a maximum speed of 2.39 m/s. Find (a) the spring constant, (b) the mass of the block and (c) the frequency of oscillation.

Answer 1

mechanical energy E = 0.872 J

Amplitude A = 10.7 cm = 0.107 m

Maximum speed V= 2.39 m/s

We know E = (1/2)mV ²

From this mass m = 2E /V ²

                           = 0.3053 kg

We know V = A

From this angular speed = V / A

                                        = 2.39 / 0.107

                                        = 22.33 rad/s

(a) the spring constant k = ?

We know k = m²

                  = 0.3053 x 22.33 ²

                  = 152.31 N / m

(b) the mass of the block m = 0.3053 kg

(c) the frequency of oscillation f = /2(pi)

                                              = 22.33 / (2x3.1415)

                                              = 3.55 Hz