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Simple Harmonic Motion (SHM) lecture
Periodic motion repeats after a fixed duration, like oscillations where a particle moves back and forth around a fixed mean position. Simple harmonic motion (SHM) is a type of periodic motion where the restoring force is directly proportional to displacement in the opposite direction. SHM includes linear and angular motions. The motion of a spring follows SHM, with displacement measured from equilibrium, amplitude as maximum displacement, and period as the time for one cycle. Any system with a restoring force proportional to negative displacement exhibits SHM, following the equation of motion that the solution has a sinusoidal form. SHM also relates to uniform circular motion, where the x-component motion is SHM. Energy in SHM systems includes potential, kinetic, and
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Simple Harmonic Motion (SHM) lecture
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- 2. Periodic Motion A motionwhich keeps repeating after fix duration of time are called periodic motion
- 3. Oscillations It is aperiodic motion in which a particle moves to & fro about a fixed point called Mean Position of Oscillations.
- 4. Simple Harmonic Motion simpleharmonic 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 1.Linear Shm 2. Angular Shm
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- 7. If an objectoscillates 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. Oscillations of a Spring
- 8. If the springis hung vertically, the only change is in the equilibrium position, which is at the point where the spring force equals the gravitational force. Oscillations of a Spring
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- 10. • Displacement ismeasured 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). Oscillations of a Spring
- 11. Any vibrating systemwhere 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: Simple Harmonic Motion How do you know? We can guess and then verify: 🡸 Velocity 🡸Acceleration
- 12. If we lookat 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. Simple Harmonic Motion Related to Uniform Circular Motion θ x
- 13. These figures illustratethe meaning of φ: φ < 0 if the nearest max is on the right.
- 14. The velocity andacceleration for simple harmonic motion can be found by differentiating the displacement: Simple Harmonic Motion
- 15. Energy in theSimple Harmonic Oscillator
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