Please see the attached file.

Question#1

According to Hook's law, the force of the spring on the handle is

Then according to Newton's law, the magnitude of the force that Gina is applying to the handle grip is 42.N as well.

Question#2

Which one of the following statements is true concerning an object executing simple
harmonic motion? Explain.

A. Its velocity is never zero
B. Its acceleration is never zero
C. Its velocity and acceleration are simultaneously zero.
D. Its velocity is zero when its acceleration is maximum.
E. Its maximum acceleration is equal to its maximum velocity.
D is correct.
The motion of the SHM can be written as
Then the velocity is
The acceleration is
The sin and cos functions are complementary. So when the velocity is zero its acceleration is maximum.
When the spring is at its maximum stretch or compress, the velocity is 0. At this time the acceleration is maximum.

Question#3

A. Determine the spring constant k.
B. How much potential energy is stored in the spring in Fig.B?
A.

The force Fs by the spring on B is equal to the weight of the block. In B, the displacement of the spring is x= -0.05m. (assuming the upward direction is positive.)
Then according to Hook's law,

The spring constant is 196N/m.
B. The potential energy stored in spring is
Question#4

Complete the following statements:

In order to increase the frequency of the motion, one would have to

A. reduce the spring constant
B. decrease the mass of the block on the end of the spring
C. increase the length of the spring
D. reduce the distance that the spring is initially stretched.
E. Increase the distance that the spring is initially stretched

Explain the following statement that you selected to be true?

The frequency of the SHM is , where k is the spring constant, m is the mass. So by decreasing the mass of the block or increasing the spring constant, the frequency will increase. B is correct.

Question#5

Which one of the following statements is true concerning the motion of the block?

A. Its acceleration is constant
B. The period of its motion depends on its amplitude
C. Its acceleration is greatest when the spring returns to the 5.0cm position
D. Its velocity is greatest when the mass has reached its maximum displacement
E. Its acceleration is greates when the mass has reached its maximum displacement.
See problem 2. The motion of the SHM can be written as
Then the velocity is
The acceleration is
A and B are obvious wrong. For D, you can also think about from the conservation of energy in SHM. The total energy of the system is . When the mass has reached its maximum displacement A, the potential energy is , thus the kinetic energy is 0. So D is wrong. Actually, the velocity is greatest when the displacement is 0.
E is the correct answer. The displacement x and the acceleration a are both in sine function. So when the displacement x is maximum, the acceleration is greatest as well. The velocity is 0 at this position.