Simple Harmonic Motion

For simple harmonic motion (SHM), the restoring force is proportional to the displacement from the equilibrium position:
By Newton's second law, , where is the acceleration. Therefore, we have:
Since acceleration , the equation becomes:
This is the differential equation of SHM, which can be written as:

Step 1: The velocity in simple harmonic motion is expressed as: where cm, cm, and rad/s.
Step 2: Substituting the given values: \bigskip

An ammeter and a voltmeter are both instruments used to measure electrical quantities, but they serve different purposes and have distinct characteristics. The differences between an ammeter and a voltmeter are as follows:
Ammeter: An ammeter measures the current flowing through a circuit. It is always connected in series with the circuit components. It has very low resistance to ensure it does not impact the current in the circuit.
Voltmeter: A voltmeter measures the potential difference (voltage) between two points in a circuit. It is always connected in parallel across the components. It has very high resistance to prevent it from drawing any current from the circuit.

The total energy of a particle undergoing simple harmonic motion is the sum of its kinetic energy and potential energy . The total energy remains constant and is given by the formula: where is the mass of the particle, is the angular frequency, and is the amplitude. The displacement of the particle is related to its amplitude as: The potential energy at displacement is given by: Substituting : Now, the kinetic energy is the difference between the total energy and the potential energy: Thus, the fraction of the total energy that is kinetic energy is: Therefore, the fraction of the total energy that is kinetic energy is . \bigskip