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If we double only the amplitude of a vibrating ideal mass-and-spring system, the mechanical energy of the system:
A. increases by a factor of 2.
B. increases by a factor of 3.
C. does not change.
D. increases by a factor of 4.
E. increases by a factor of √2.

Respuesta :

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

[tex]V=\dfrac{dx}{dt}[/tex]

V= A ω cosωt

The mechanical energy of spring mass system

[tex]U=\dfrac{1}{2}KA^2[/tex]

K=Spring constant

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

Therefore the answer is D.

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