CGPET 2021 Solved Paper

Given, potential energy, U=2.5J
If mass of particle be m
and amplitude be a, then
U=

1

2

mω2a2⇒2.5=

1

2

mω2a2
∴ mω2a2=5 ..........(i)
According tom the problem, the position of particle from mean position is given as
x=

a

2

Thus, the total energy,
T=(potential‌energy)+(kinetic‌energy)
=

1

2

mω2x2+

1

2

mω2(a2−x2)
=

1

2

mω2(

a

2

)2+

1

2

mω2[a2−(

a

2

)2]
=

1

2

mω2a2=

1

2

×5[ From eq.(i)]
=2.5J