Question

A 5kg mass is hung from the end of a coil spring. If the system is made to vibrate without simple harmonic motion (SHM) with a period of 2 seconds, what is the energy of the motion if the amplitude of vibration is 3cm?

a) 15 J
b) 30 J
c) 45 J
d) 60 J

Answer 1

The energy of the motion is 0.45 J.

Step-by-step explanation:

To find the energy of the motion, we can use the equation for the energy of simple harmonic motion (SHM):

E = (1/2) k A2

where E is the energy, k is the spring constant, and A is the amplitude of vibration.

In this case, the amplitude is 3 cm, which is equal to 0.03 m. The spring constant can be calculated using the formula:

k = (2π/T)2 m

where T is the period of the motion. In this case, T = 2 s.

Plugging these values into the equation:

E = (1/2) ( (2π/2)2 )(0.03)2 = 0.45 J

Therefore, the energy of the motion is 0.45 J, which is closest to option c) 45 J.