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 .
B) increases by a factor of 2.
C) increases by a factor of 3.
D) increases by a factor of 4.
E) does not change.

Question

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 . 
B) increases by a factor of 2. 
C) increases by a factor of 3. 
D) increases by a factor of 4. 
E) does not change.

Quizplus · Accepted Answer

The mechanical energy of an ideal mass-and-spring system is proportional to the square of the amplitude. Therefore, doubling the amplitude will increase the mechanical energy by a factor of (2^2) = 4. Option (D) is the only one that predicts a factor of 4 increase. Option (A) is incorrect, as it suggests a non-integer factor increase. Option (B) is incorrect, as it predicts a linear relationship between amplitude and energy. Option (C) is incorrect, as it predicts a super-linear relationship between amplitude and energy. Option (E) is not correct, as the mechanical energy of the system does in fact change with a change in amplitude.

If We Double Only the Amplitude of a Vibrating Ideal