Physics, asked by syeddanish1, 11 months ago

show the motion of a simple pendulum is simple Harmonic and hence derive an equation for its time period

Answers

Answered by RadhikaParwal

Answer:

● Motion of pendulum as SHM -

[Refer to the figure]

Consider a simple pendulum with mass m and length l.

Let y and θ be its linear and angular displacements respectively.

θ = y/l

At extreme position,

Tangential acceleration is-

a = gsinθ

Torque about point of suspension is-

τ = -Fl

τ = -l(mgsinθ)

M.I. is related by-

τ = Iα

-l(mgsinθ) = Iα

When, θ is small, sinθ = θ,

α = -lmgθ/I

Comparing this with std eqn of SHM ω = √(mgl/I),

We can say that pendulum shows SHM.

● Period of oscillation-

T = 2π/ω

T = 2π/√(mgl/I)

Here, I = ml^2

T = 2π/√(mgl/ml^2)

T = 2π√(l/g)

Hope that was useful...

Explanation:

Answered by ElegantDoll

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❤. SIMPLE PENDULUM: A metalic bob suspended by a light , torsionless, inextensible string is called simple pendulum.

❤. SECONDS PENDULUM : A pendulum with time period 2seconds is called seconds pendulum

❤. Kindly refer the above attachment

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