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Simple Harmonic Motion(SHM) Lecture 1

This presentation consists of basics of linear simple harmonic motion.

shriyeshgautam
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Simple Harmonic Motion(SHM) Lecture 1

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  1. SHM LECTURE

  2. Periodic Motion A motion which keeps repeating after fix duration of time are called periodic motion

  3. Oscillations It is a periodic motion in which a particle moves to & fro about a fixed point called Mean Position of Oscillations.

  4. Simple Harmonic Motion simple harmonic motion is a special type of periodic motion or oscillation where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.

  5. TYPES OF SHM • Linear Shm 2. Angular Shm

  6. ANALYSIS OF SHM

  7. Oscillations of a Spring If an object oscillates back and forth over the same path, each cycle taking the same amount of time, the motion is called periodic. The mass and spring system is a useful model for a periodic system.

  8. Oscillations of a Spring If the spring is hung vertically, the only change is in the equilibrium position, which is at the point where the spring force equals the gravitational force.

  9. Restoring Force F= -kx

  10. Oscillations of a Spring • Displacement is measured from the equilibrium point. • Amplitude is the maximum displacement. • A cycle is a full to-and-fro motion. • Period, T, is the time required to complete one cycle. • Frequency, f, is the number of cycles completed per second. The unit of frequency is Hz (cycles per second).

  11. Simple Harmonic Motion Any vibrating system where the restoring force is proportional to the negative of the displacement is in simple harmonic motion (SHM), and is often called a simple harmonic oscillator (SHO). Substituting F = -kx into Newton’s second law gives the equation of motion: The solution has the form: How do you know? We can guess and then verify: 🡸 Velocity 🡸Acceleration

  12. Simple Harmonic Motion Related to Uniform Circular Motion If we look at the projection onto the x axis of an object moving in a circle of radius A at a constant angular velocity ω, we find that the x component of the circular motion is in fact a SHM. θ x

  13. These figures illustrate the meaning of φ: φ < 0 if the nearest max is on the right.

  14. Simple Harmonic Motion The velocity and acceleration for simple harmonic motion can be found by differentiating the displacement:

  15. Energy in the Simple Harmonic Oscillator

  16. Potential Energy of SHM

  17. Total Energy of SHM

  18. THANK YOU

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