Question

If we double only the amplitude of a vibrating ideal mass-and-spring system, the mechanical energy of the system:

Answer 1

Answer:

D. increases by a factor of 4.

Explanation:

General equation of SHM

Lets taken the general equation of the displacement given as

x = A sinω t

A=Amplitude ,t=time ,ω=natural frequency

We know that speed V

$V=\dfrac{dx}{dt}$

V= A ω cosωt

The mechanical energy of spring mass system

$U=\dfrac{1}{2}KA^2$

K=Spring constant

Now when Amplitude A become 2 times then the mechanical energy will become 4 times.

Therefore the answer is D.