Question

A particle executes simple harmonic motion with the period 8 second find the time in which half the of the total energy is potential energy

Answer 1

If particle execute simple harmonic motion, equation of motion of particle is

potential energy, P.E = F.dx

= 1/2m

And total energy, T.E = 1/2 mA²

Now, A/C to question,

P.E = 1/2(T.E)

1/2m = 1/2(1/2 mA²)

x = A/√2

Now,

A/√2 = Asint

= π/4

so, 2π/T × t = π/4

Given, T = 8 sec

then, 2π/8 × t = π/4

t = 1 sec

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Answer 2

Answer:

1sec

Explanation:

Data:

T=8sec

Find : time=?

solution:

P. E = 1/2 mw^2x^2

and T.E=1/2 mw^2a^2

Now acc. to que

P. E =1/2T.E

1/2mw^2x^2=1/2mw^2a^2

now to calculate it

by using the formula of x=asinwt

... ..... ..... ......

t= 1sec