Energy in SHM: 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

Energy in SHM: 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 a vibrating mass-and-spring system is proportional to the square of the amplitude (E = 1/2 kA^2). If we double the amplitude, the mechanical energy increases by a factor of (2)^2 = 4. Therefore, the correct answer is D.

Energy in SHM: If We Double Only the Amplitude of a Vibrating