Answered: Simple Harmonic Motion is defined as a…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.3P

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Question

Simple Harmonic Motion is defined as a periodic motion of a point along a straight line,
such that its acceleration is always towards a fixed point in that line and is proportional to
its distance from that point. In other words, its acceleration is proportional to the
displacement but acts in an opposite direction. Prove algebraically that the motion of a
particle defined by x=cos2t + 2sin2t is simple harmonic.

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

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