Question

if the amplitude of the simple harmonic motion of a mass-spring system is doubled, the mechanical energy of the system:

a. decreases by a factor of 2

b. increases by a factor of 2

c. increases by a factor of sqrt(2)

d. increases by a factor of 4

e. decreases by a factor of 4.

f. decreases by a factor of sqrt(2)

g. does not change

Answer 1

total mechanical energy = E = 1/2 * K * A^2

if the amplitude is doubled E1 = 1/2 * K * (2A)^2

                                        E1 = 4 E

                              increases by a factor of 4