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 a mass-and-spring system is given by the equation E = (1/2)kA^2, where k is the spring constant and A is the amplitude of the vibration. Doubling the amplitude (i.e., making A -> 2A) results in E = (1/2)k(2A)^2 = 2(1/2)kA^2 = 2E. Therefore, the mechanical energy of the system increases by a factor of 2^1 = 4. Therefore, the correct answer is (D).

If We Double Only the Amplitude of a Vibrating Ideal