What is a simple pendulum? Show that a vibrating simple pendulum performs SHM. What is the formula for the time period of a simple pendulum? On what factors does it depend?

A simple pendulum consists of a small mass (bob) attached to a string of fixed length, suspended from a rigid support. When displaced slightly, it oscillates back and forth under the influence of gravity.

Derivation of SHM for a simple pendulum:

The restoring force acting on the bob is:

F=-mg sinθ

For small angles (θ=sinθ), the equation simplifies to:

a= -gx/l
Since acceleration is directly proportional to displacement and directed toward the mean position, the motion is SHM.

Time Period Formula:

T=2π√l/g
Factors affecting the time period:

Length of the pendulum (l): A longer pendulum increases the time period.

Acceleration due to gravity (g): A higher gravitational field strength decreases the time period.

Related Questions:

  1. What do you mean by oscillation? Define simple harmonic motion. What are the conditions for a body to perform SHM? Give examples of bodies that perform SHM.
  2. Show that a vibrating mass-spring system performs simple harmonic motion. What is its time period? On what factors does it depend?
  3. Explain the following terms for SHM: Vibration, amplitude, time period, frequency.
  4. Explain that a steel ball dropped from the edge of a shining bowl performs SHM.
  5. Simple harmonic motion and waves
  6. Simple harmonic motion and waves-NFE
  7. Give an example of vibratory motion which is not simple harmonic motion. Give a reason for your selection.
  8. At the extreme position, velocity is zero but acceleration is maximum in simple harmonic motion. How can you theoretically explain it?
  9. What will happen to the acceleration of a mass-spring system if its mass is doubled?
  10. A simple pendulum has a time period “T”. What will happen to its time period if its thread length is shortened to half?
  11. A simple pendulum has a time period of 4 seconds. Will its time period remain the same or change if its steel bob is replaced by a wooden bob of the same size?
  12. Same masses are attached to different springs, one is vibrating faster. Why?
  13. A simple pendulum has a time period “T” in Murree. In Karachi, it has a different time period. What would you do to make its time period the same as it was in Murree?
  14. What will happen to the frequency of waves in a ripple tank if the time period of the electrical vibrator is decreased? What will happen to the wave speed?
  15. Why do water waves refract at the boundary of shallow water and deep water in a ripple tank experiment?
  16. Under what conditions are waves diffracted the most?