Charterstics of Simple harmonic motion Assignment Help

Assignment Help: >> Simple Harmonic Motion >> Charterstics of Simple harmonic motion

(i) Amplitude: It is the largest value of distance of the particle from its equilibrium position.

(ii) Time period (T): Smallest time interval after which the oscillatory motion gets repeated is called Time period.

(iii) Frequency (f): Number of oscillations completed in unit time interval is called frequency of oscillations, 2191_Charterstics of Simple harmonic motion.png. Its units is sec-1 or Hz.

(iv) Angular Frequency (w): The quantity  is called the angular frequency of the oscillating object. As we see that second order differential equation of simple harmonic motion is 1761_Charterstics of Simple harmonic motion1.png   is called angular frequency and its units is rad/sec.

(v) Phase: The physical quantity which represents the state of motion of particle [eg. its position and direction of motion (orientation)] at any instant of time is called phase of that physical quantity.

In the solution of second order differential equation of SHM,  is called phase of the motion.

(vi) Displacement (x) : If time is measured from the equilibrium phase, distance x from equilibrium point at any instant of time t is given by x = Asinωt

(vii) Velocity (v):1340_Charterstics of Simple harmonic motion2.png

            or             1406_Charterstics of Simple harmonic motion3.png

(a) Velocity is minimum at extreme positions and is zero.

            At  x = A,          v = vmin = zero.

(b) Velocity is maximum at the equilibrium position and is wA.

            At  x = 0,          v = vmax = ωA

(c) Direction of speed is either towards or away from the equilibrium position.

(viii) Acceleration (a) =  549_Charterstics of Simple harmonic motion4.png

(a) The lowest value of acceleration is zero and it occurs at equilibrium.

(b) The maximum value of acceleration is ω2A and it occurs at extreme positions.

(c) Acceleration is usually directed towards the equilibrium position and so it is always opposite to the direction of the displacement.

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