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Simple harmonic motion And its application
This presentation introduces simple harmonic motion (SHM) and its applications. SHM describes a back-and-forth motion where the restoring force is directly proportional to displacement from the equilibrium position. One example is the motion of a spring according to Hooke's law, where the force is proportional to displacement. SHM has a differential equation and solutions that describe oscillations with a characteristic frequency and period. Common applications that exhibit SHM include springs, pendulums, and torsional oscillators.
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Simple harmonic motion And its application
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- 2. SIMPLE HARMONIC MOTION ANDITS APPLICATION PRESENTED BY MD. SUMON SARDER ID: 161-15-953
- 3. SIMPLE HARMONIC MOTION BACKAND FORTH MOTION WHICH IS CAUSED BY A FORCE THAT IS DIRECTLY PROPORTIONAL TO THE DISPLACEMENT. THE DISPLACEMENT CENTERS AROUND AN EQUILIBRIUM POSITION. xFs
- 4. Springs – Hooke’sLaw kxorkxF k k xF s s N/m):nitConstant(USpring alityProportionofConstant One of the simplest type of simple harmonic motion is called Hooke's Law. This is primarily in reference to SPRINGS.
- 5. Simple Harmonic Motion(SHM) Hence, In SHM the restoring force is proportional to the displacement and acts in the opposite direction of that displacement
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- 7. Value of 𝜔 Puttingthe solution in the differential equation we get the value of 𝜔 𝑑2 𝑥 𝑑𝑡2 + 𝑘 𝑚 𝑥 = 0 −𝜔2 𝐴𝑐𝑜𝑠 𝜔𝑡 + 𝜙 + 𝑘 𝑚 𝐴𝑐𝑜𝑠 𝜔𝑡 + 𝜙 = 0 𝜔 = 𝑘 𝑚
- 8. Time Period ofSHM If we increase the time t in the solution of SHM by 2𝜋/𝜔, the function becomes, 𝑥 = 𝐴𝑐𝑜𝑠 𝜔 𝑡 + 2𝜋 𝜔 + 𝜙 = 𝐴𝑐𝑜𝑠 𝜔𝑡 + 2𝜋 + 𝜙 = 𝐴𝑐𝑜𝑠 𝜔𝑡 + 𝜙 i.e. the function repeats itself after a time 2𝜋/𝜔 Therefore 2𝜋/𝜔 is the period of the motion, T. 𝑇 = 2𝜋 𝜔 𝜔 = 2𝜋 𝑇 = 2𝜋𝑓, is the angular frequency.
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- 12. Applications of SHM Asper Hooke’s law the restoring force on a spring is F=-kx, the exact condition for simple harmonic oscillation.
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- 15. The Physical Pendulum Ifwe locate the pivot far from the object , using a weightless cord of length L, we would have, 𝐼 = 𝑀𝐿2 𝑎𝑛𝑑 ℎ = 𝐿 Then, 𝑇 = 2𝜋 𝐼 𝑀𝑔ℎ = 2𝜋 𝑀𝐿2 𝑀𝑔𝐿 = 2𝜋 𝐿 𝑔 Which is the period of a simple pendulum!
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