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PHYSICS LAB EXPERIMENT : Simple Harmonic Motion

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PHYSICS

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PHYSICS

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Uploaded on October 31, 2023
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physics lab experiment simple harmonic motion

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I. OBJECTIVE

To study the behaviour of oscillations (Simple Harmonic Motion) in situation where there is

resistive force of fluid investigated by study of exponential amplitude decay in the fluid as

compared to relatively undamped environment of air.

II. HYPOTHESIS

During Simple Harmonic Motion (SHM) in damped fluid environment amplitude of

oscillation decreases exponentially. And the rate of amplitude decay depends on viscosity of

fluid medium.

III. THEORY

Simple Harmonic Motion (SHM), is a type of motion in which there is an restoring force

which is always directed towards a unique point. In ideal conditions force equations on a

object undergoing SHM is given by Hooke’s law,

F = -kx

Where, x is displacement from 0 stretch of spring and,

k is the spring constant of the spring.

Upon solving above equation, general form of the displacement, for SHM can be given as,

x = Acos(wt+Φ)

where, A is amplitude,

w is angular frequency and,

Φ is phase of the oscillation.

, w = √(k/m) , k is spring constant and m = mass of attached material to spring

T = 2π/w, T is time period

Thus, velocity of an object undergoing SHM can be written as,

v = -wAsin(wt+Φ) , v is velocity.

Now, if there is a fluid in the system this the resistivity of fluid can be defined as viscosity.

This viscosity provides the damping influence on the SHM and due to resistance dissipates

the energy of SHM making its amplitude smaller, and smaller, and this damping influence

can be given analysed using,

F = -kx-Fdamping

and Fdamping = -bv , b is drag constant, generally representative of viscosity and friction always

acting opposite of the motion.

Upon solving above equation,

we get, x = Ae(-b/2m)cos(wt+Φ)

Also, w = sqrt(wo2-b2/(4m2))

and, wo =sqrt(k/m)

Thus it can be said from above equations that damping reduces both the amplitude and

angular frequency with time for a damped SHM. Also it should be noted that as b in increases

the amplitude decreases by the factor of exponential factor of b. Hence it can be predicted

that for fluids with larger viscosity rate of decay of Amplitude will be larger.

Also, it should be noted that viscosity, b = 2[ps – pl]*ga2/(9v)

where, a is radius of sphere or a2 is surface area on which resistive force of fluid is acting.

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