find an expression for the acceleration of a simple harmonic oscillator
Answers
Answered by
0
We know what acceleration is. It is velocity per unit time. We can calculate the acceleration of a particle performing S.H.M. Lets learn how. The differential equation of linear S.H.M. is d2x/dt2 + (k/m)x = 0 where d2x/dt2 is the acceleration of the particle, x is the displacement of the particle, m is the mass of the particle and k is the force constant. We know that k/m = ω2where ω is the angular frequency.
Therefore, d2x/dt2 +ω2 x = 0
Hence, acceleration of S.H.M. = d2x/dt2 = – ω2 x (I)
The negative sign indicated that acceleration and displacement are in opposite direction of each other. Equation I is the expression of acceleration of S.H.M. Practically, the motion of a particle performing S.H.M. is accelerated because its velocity keeps changing either by a constant number or varied number.
Take a simple pendulum for example. When we swing a pendulum, it moves to and fro about its mean position. But after some time, it eventually stops and returns to its mean position. This type of simple harmonic motion in which velocity or amplitude keeps changing is damped simple harmonic motion.
Therefore, d2x/dt2 +ω2 x = 0
Hence, acceleration of S.H.M. = d2x/dt2 = – ω2 x (I)
The negative sign indicated that acceleration and displacement are in opposite direction of each other. Equation I is the expression of acceleration of S.H.M. Practically, the motion of a particle performing S.H.M. is accelerated because its velocity keeps changing either by a constant number or varied number.
Take a simple pendulum for example. When we swing a pendulum, it moves to and fro about its mean position. But after some time, it eventually stops and returns to its mean position. This type of simple harmonic motion in which velocity or amplitude keeps changing is damped simple harmonic motion.
Similar questions