1 (a). Examine. with practicals examples, the general form of a particle undergoing sinmple harmonic motion...

1 (a). Examine. with practicals examples, the general form of a particle undergoing sinmple harmonic motion and carefully explain all the associated terms

Expert Solution

simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.

Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law

Mathematically, the restoring force F is given by

where F is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m⁻¹), and x isthe displacement from the equilibrium position (in m).

For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, can be obtained by means of Newton's second law (and Hooke's law for a mass on a spring).

where m is the inertial mass

The kinetic energy K of the system at time t is

and the potential energy is

Mass of a simple pendulum The period of a mass attached to a pendulum of length ℓ with gravitational acceleration g is given by

genius_generous answered 8 months ago

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