Question

Define simple harmonic motion and state the relationship between displacement from its mean position and the restoring force when a body executes simple harmonic motion. A body is supported by a helical spring and causes an extension of (1.5 , {cm}) in the spring. If the mass is set into vertical oscillation, calculate the period of the oscillation. (Ans: (0.25 , {s})).

Answer 1

Simple harmonic motion is oscillatory motion where the restoring force is proportional to the displacement. In the given scenario, the period of the oscillation can be calculated using the formula T = 2π√(m/k), where m and k are the mass and force constant, respectively. The period of the oscillation is 0.25 seconds (s).

Step-by-step explanation:

Simple Harmonic Motion

Simple harmonic motion (SHM) is oscillatory motion for a system where the restoring force is proportional to the displacement and acts in the direction opposite to the displacement. The relationship between displacement and the restoring force in simple harmonic motion is that the restoring force is directly proportional to the displacement. This means that as the displacement increases, the restoring force also increases.

Calculating the Period of Oscillation

Given an extension of 1.5 cm in the spring and assuming a mass is set into vertical oscillation, we can calculate the period of the oscillation. The period T of a simple harmonic oscillator can be calculated using the formula T = 2π√(m/k), where m is the mass and k is the force constant. Substituting the values, we get T = 2π√(m/1.5).

Using this formula, the period T of the oscillation is 0.25 seconds (s).