Question

When the maximum kinetic energy of a simple pendulum is k then what is its displacement in terms of amplitude a when its ke is k/2

Answer 1

Answer:

distance will be A/(2)1/2

Answer 2

Answer:

The kinetic energy expression for a simple pendulum is given as

KE = 1/2*m*w^2(a^2-x^2)

Clearly, from the given function the kinetic energy will be maximum at the mean position that is at x = 0

So, that

K = 1/2*mw^2a^2

Now,

when Kinetic energy is K/2

Putting this in kinetic energy expression to get the value of x

We get

K/2 = 1/2mw^2(a^2 - x^2)

Now

1/2(1/2mw^2a^2) = 1/2mw^2(a^2-x^2)

Which means,

x = +- a/√2

So, at this Value of distances on either side of the mean position the Kinetic energy will be half of the maximum available Kinetic energy.