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A particle of mass 2kg executing SHM has...

A particle of mass 2kg executing SHM has amplitude 20cm and time period 1s. Its maximum speed is

A

amplitude of oscillation is approximately 2.53 m

B

minimum potential energy of the particle is 2 J

C

maximum acceleration of the particle is approximately `6.3 ms^(-2)`

D

minimum kinetic energy of the particle is 2 J

Text Solution

Verified by Experts

The correct Answer is:
A, C
(a,c) Maximum kinetic energy =energy of oscillation in SHM
`therefore 8=(1)/(2)kA^(2)`
`therefore kA^(2)=16" "(i)`
Further, `2pisqrt((m)/(k))=4 " "(because T=4 s)`
`therefore (1)/(k)=(4)/(pi^(2))`
or `k=(pi^(2))/(4)" "...(ii)`
From Eqs. (i) and (ii) we get,
`k~~2.5 Nm^(-1)`
and `A~~253m`
Maximum acceleration of the particle will be
`a_("max")=omega^(2)A=(k)/(m)A`
`=((2.5)/(1))(2.53)~~6.3 ms^(-2)`
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