A pendulum has a length of 1 m. What is the period of this pendulum? What is the

Question

A pendulum has a length of 1 m. What is the period of this pendulum? What is the frequency of this pendulum? You measure the period of a pendulum and get 25s. What is the length of the pendulum? If your grandfather clock was running "slow" how would you adjust the bob? How would the period of a pendulum that is 1m long change if you go to the moon? If you double the mass of a pendulum bob, but everything else is kept the same, how does the period change? Why should you keep the amplitude of a pendulum small?

Explanation / Answer

a)

time period = T = 2*pi*sqrt(L/g)

T = 2*pi*sqrt(1/9.8) = 2 s

b)

T = 25 s

25 = 2*pi*sqrt(L/9.8)

L = 155.14 m

(c)

time is slow means time period is more.

so the length is decreases to keep the time correct

(d)

on moon = g = 9.8/6

T' = 2*pi*sqrt(6/9.8)

T' = 4.92 s

(e)

time period does not depend on mass

time period remains same

(f)

The component perpendicular to the length accelerates the bob,

m*l^2*(dtheta/dt)^2 = - m*g*sintheta

For small angles, the equation is close to that for a simple harmonic oscillator,

m*l^2*(dtheta/dt)^2 = - m*g*theta

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