A mass-spring system on a horizontal frictionless surface is set in simple harmonic motion with amplitude A.The mass is then doubled and the system is again set into simple harmonic motion with the same amplitude.Which of the following is true about the total mechanical energy of the system due to doubling the mass?
A)It has doubled.
B)It has quadrupled.
C)It has halved.
D)It has not changed.

Question

Quizplus · Accepted Answer

The total mechanical energy of a simple harmonic oscillator is given by:

E = (1/2)kA^2

where k is the spring constant and A is the amplitude. Since the surface is frictionless, there is no energy loss due to friction.

When the mass is doubled, the spring constant is also doubled to keep the frequency of oscillation the same. Therefore, the total mechanical energy of the system remains the same:

E = (1/2)(2k)A^2 = (1/2)k(2A)^2 = (1/2)kA^2

Thus, the answer is D - the total mechanical energy has not changed.

A Mass-Spring System on a Horizontal Frictionless Surface Is Set