Part A:

A mass of 210 g oscillates on a horizontal frictionless surface at a frequency of 2.2 Hz and with amplitude of 5.0 cm.

Find the effective spring constant for this motion.

Thus, the motion is simple harmonic motion.

Here ,  Hz and .

For horizontal frictionless surface,

Frequency of  object in simple harmonic motion is  .

Substitute corresponding values in .

N/m.

Part B:

Find the energy involved in the motion.

Energy involved in simple harmonic motion is .

From part A, N/m and

Substitute corresponding values in .

.

From the Hooks law : .

Where, is the restoring elastic force exerted by the spring and is  the displacement from the equilibrium position and is effective spring constant.

Substitute and m/s² in .

.

Substitute corresponding values in .

.

Negative sign is because spring pulls up and stretch is down.

Substitute corresponding values in .

N/m.

Spring stiffness constant is N/m.

Part B:

When the fish is hung from the scale, it defines the equilibrium position at 3.1 cm.

When the fish is pulled down an additional distance, the initial amplitude of oscillation is then established to be 2.8 cm.

Thus, amplitude of vibration is 2.8 cm.

Part C:

A fishermans scale stretches 3.5 cm when a 2.2 kg fish hangs from it.

Find the frequency of vibration if the fish is pulled down 2.8 cm more and released so that it vibrates up and down.

Thus, the motion is simple harmonic motion.

Frequency of  object in simple harmonic motion is  .

From part A, N/m and kg.

Substitute corresponding values in .

Thus, the frequency of vibration is 2.66 Hz.