define simple harmonic motion. derive an expression for the potential energy and K.E of a harmonic oscillator. hence show that total energy remains conserved in S.H.M
Asked by futureisbright051101
5th March 2018,
7:30 PM
Answered by Expert
Answer:
If an object is under oscillating motion and at any instant the force acting on it is proportional to its displacement from equilibrium position, then such an oscillating motion is called Simple harmonic motion (SHM).
Mathematically F(x) = -k×x....................(1)
where k is constant and negative sign indicates direction of force and direction of displacement are opposite.
Equation (1) can be rewritten by using the definition of force = mass times acceleration
where x is displacement, xm is amplitude of SHM, ω is angular frequency;
ω= 2πf where f is the frequency of oscillation and Φ is phase constant.
hence total energy is constant
Answered by Expert
6th March 2018,
10:22 AM
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