Question

Five different experiments are carried out. In each experiment, a block is attached to a horizontal spring. The block is pulled back a certain distance and released. The block oscillates back and forth on a frictionless surface. Rank the amplitude of oscillation for each of the following situations. (Rank the smallest amplitude as 1).
1) A block of mass M is attached to a spring with a spring constant k, pulled back a distance 2d, and released.
2) A block of mass M is attached to a spring with a spring constant 2k, pulled back a distance (1/2)d, and released.
3) A block of mass (1/2)M is attached to a spring with a spring constant k, pulled back a distance d, and released.
4) A block of mass M is attached to a spring with a spring constant 2k, pulled back a distance d, and released.
5) A block of mass M is attached to a spring with a spring constant k, pulled back a distance d, and released.

Answer 1

The maximum amplitude is simply equal to the distance the block is pulled back.
max = 2d
The amplitude of the 2M block = the amplitude of the M block with the 2k spring constant = the amplitude of the M block with the k spring constant = d
min = 1/2d

In SHM problems the energy is conserved and is a combination of spring PE and KE.
E = Spring PE + KE
E = 1/2*k*x^2 + 1/2*m*v^2

Initially when the block is moved back, right before it is released it is not moving, so v = 0.
E = 1/2*k*x^2

Since the energy is not changing, x will never be more than it is when it is pulled back.
E = 1/2*k*A^2

During it's motion, when it passes the neutral axis the spring becomes relaxed, so there is no more spring PE and KE is maxed out
E = 1/2*m*v_max^2

So, as you can see, the mass, the spring constant, and the distance pulled back, A, affect the the energy of the system, but the energy of the system will never increase to get it past A... unless a force is applied. Hope the explanation helped