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Consider a spring that exerts the follow...

Consider a spring that exerts the following restoring force :
`F = -kx` for `x ge 0`
`F = -4kx` for `x lt 0`
A mass m on a frictionless surface is attached to the spring displaced to `x = A` by strectching the spring and released :

A

The period of motion will be `T = (3)/(2)pi sqrt((m)/(k))`

B

The most negative value of `x` the mass m can reach will be `x = -(A)/(2)`

C

The time taken to move from `x = A` to `x = +(A)/(sqrt(2))` , straight away will be equal to `(5pi)/(8) sqrt((m)/(k))`

D

The total energy of oscillations will be `(5)/(2)kA^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Consider a ………….
`T = (1)/(2)(2pi sqrt((m)/(k))+2pi sqrt((m)/(4k)))`
`T = (3)/(2)pi sqrt((m)/(k))`
`(1)/(2) kA^(2)=(1)/(2)4kA^(2) implies A'(A)/(2)` .
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