If we double only the spring constant 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 spring constant 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 E = (1/2)kA^2, where k is the spring constant and A is the amplitude of the oscillation. If we double the spring constant while keeping the amplitude constant, the mechanical energy of the system would increase by a factor of (k_new/k_old)(A^2/A^2) = k_new/k_old = 2/1 = 2. Therefore, the correct answer is B, which states that the energy increases by a factor of 2.

If We Double Only the Spring Constant of a Vibrating