For an oscillating simple pendulum the tension in the string is maximum at the mean position and minimum at the extreme position.

Question

Verified by Toppr

Answer 1

In simple pendulum, when bob is in deflection position, the tension in the string is $T = m g cos θ + \frac{m v ^{2}}{l}$ . Since the value of $θ$ is different at different positions, hence tension in the string is not constant throughout the oscillation. At end points $θ$ is maximum; the value of $cos θ$ is least, hence the value of tension in the string is least. At the mean position,the value of $θ = 0^{o}$ and $cos 0^{o} = 1$ , so the value of tension is largest. Also velocity is given by $v = ω a^{2} - y^{2}$ which is maximum when $y = 0$ , at mean position.

Answer 2

In simple pendulum, when bob is in deflection position, the tension in the string is

T = m g cos θ + \frac{m v ^{2}}{l}

. Since the value of

θ

is different at different positions, hence tension in the string is not constant throughout the oscillation. At end points

θ

is maximum; the value of

cos θ

is least, hence the value of tension in the string is least. At the mean position,the value of

θ = 0^{o}

and

cos 0^{o} = 1

, so the value of tension is largest. Also velocity is given by

v = ω a^{2} - y^{2}

which is maximum when

y = 0

, at mean position.