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 given by the equation E = (1/2) k A^2, where k is the spring constant and A is the amplitude of the oscillation. Doubling the amplitude (i.e. A --> 2A) results in an increase in mechanical energy by a factor of 4 [(1/2) k (2A)^2 / (1/2) k A^2 = 4]. Therefore, the correct answer is D, which states that the energy increases by a factor of 4.

If We Double Only the Amplitude of a Vibrating Ideal