## Theory of SHM and Waves

This page consists of theory, examples, assignments and Comprehensive Questions included in unit 10, SHM and Waves for grade 10.

**Topics, Questions, Examples, and Assignments**

**Oscillations**

**Question: Define Oscillatory motion and the terms associated with oscillation.**

#### Example 10.1: What is the frequency of oscillation if the time period is 20 ms?

**Assignment 10.1: When an object oscillates with a frequency of 0.5 Hz, what is its time period?**

**Simple Harmonic Motion**

**Question: What is simple harmonic motion? Explain the conditions necessary for a body to oscillate with SHM.**

**SHM … Mass-spring system**

**Question: What is spring-mass system in Physics? Show that a mass attached to a spring executes SHM.**

**Question: Derive expressions for the time period and frequency of mass-spring system.**

#### Example 10.2: A spring has a spring constant 48.0 N/m. This spring is pulled to a distance of 55 cm from equilibrium. What is the restoring force?

**See Answer****Assignment 10.2: Determine the restoring force of a spring displaced 1.5 m with the spring constant of 30.0 N/m.**

#### Example 10.3: What is the mass of a vertical mass-spring system if it oscillates with a period of 2.0 s and has spring constant of 20.0 N/m.

**See Answer****Asignment 10.3:A body of mass 0.2 kg is attached to a spring placed on a frictionless horizontal surface. The spring constant of the spring is 4 N/m. Find the time period of the oscillating mass-spring system.See Answer**

**SHM …Simple Pendulum**

**Question: What is simple pendulum? Diagramically show the forces acting on a simple pendulum. Show that a simple pendulum executes Simple Harmonic Motion.**

**Question: Derive expressions for the time period and frequency of a simple pendulum.**

#### Example 10.4: Determine the magnitude of the restoring force for a pendulum bob of mass 100.0 g that has been pulled to an angle of 10° from the vertical.

**See Answer****Asshignment 10.4: At what angle must the pendulum be displaced to create a restoring force of 4.00 N on a bob with a mass of 500.0 g?See Answer**

#### Example 10.5: What is the gravitational field strength at planet Mercury, if a 0.500 m pendulum swings with a period of 2.30 s?

**See Answer****Assignment 10.5: What is the gravitational field strength at the top of Mount Everest at an altitude of 8954.0 m, if a pendulum with a length of 1.00 m has a period of 2.01 s?See Answer**