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Basics of Simple Harmonic Motion
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Some basic concepts such as frequency, time period and phase for SHM

Dr Dushyant Pradeep
I have done Ph.D. in Physics. Presently working in Jammu as a Physics Teacher, Earlier worked as Asst. Prof. in LPU and I Love teaching Phys

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  1. Dr. Dushyant Pradeep Ph.D. Physics, B.Ed Presently working in Jammu as a Principal, Earlier worked as Assistant Professor in, Lovley Professional Universit and MIET; Guest Faculty in HNB Garhwal (A Central University) University, Teaching Experience -08 Years


  2. Basics of Simple Harmonic Motion


  3. Periodic Motion Periodic motion is motion of an object that regularly returns to a given position after a fixed time interval A special kind of periodic motion occurs in mechanical systems when the force acting on the object is proportional to the position of the object relative to some equilibrium position If the force is always directed toward the equilibrium position, the motion is called simple harmonic motion


  4. Motion of a Spring-Mass System A block of mass m is attached to a spring, the block is free to move on a frictionless horizontal surface oC Use the active figure to vary the initial conditions and observe the resultant motion 0C e When the spring is neither stretched nor compressed, the block is at the equilibrium position oc 0C


  5. Hooke's Law Hooke's Law states F, =-kx F, is the restoring force It is always directed toward the equilibrium position Therefore, it is always opposite the displacement from equilibrium k is the force (spring constant o x is the displacement


  6. Simple Harmonic Motion Mathematical Representation e Model the block as a particle The representation will be particle in simple harmonic motion model Choose x as the axis along which the oscillation occurs Accelerationxk 2 d t . Then a = _orx


  7. Simple Harmonic Motion - Mathematical Representation, 2 A function that satisfies the equation is needed o Need a function x(t) whose second derivative is the same as the original function with a negative sign and multiplied by o The sine and cosine functions meet these requirements


  8. Simple Harmonic Motion - Graphical Representation A solution is x(t) A cos (at + . A, , are all constants A cosine curve can be used to give physical significance to these constants -A


  9. Simple Harmonic Motion Definitions A is the amplitude of the motion o This is the maximum position of the particle in either the positive or negative direction is called the angular frequency o Units are rad/s is the phase constant or the initial phase angle


  10. Simple Harmonic Motion, cont A and are determined uniquely by the position and velocity of the particle at t = 0 If the particle is at x =A at t = 0, then = 0 The phase of the motion is the quantity (ot x (t) is periodic and its value is the same each time o t increases by 2 radians