CGPET 2019 Solved Paper

We know that, displacement at t is given by
y=a‌sin‌ω‌t ........(i)
∴ Velocity, v=aω‌cos‌ω‌t .......(ii)
Here, a= amplitude
and ω= angular frequency =

2π

T

.
∴cos‌ω‌t=cos(

360

T

×

T

12

) =cos‌30°=

√3

2

From Eq. (i), we get
Velocity, v=

√3

2

aω .......(iii)
Kinetic energy (KE)=

1

2

mv2
From Eq. (iii), we get
=

1

2

ma2

3

4

ω2=

3

8

ma2ω2 .........(iv)
As we know that
Total energy (TE)=

1

2

ma2ω2 .........(v)
∴ Potential energy =TE−KE
=

1

2

ma2ω2−

3

4

ma2ω2
=

1

2

ma2ω2[1−

3

4

]
=

1

2

ma2ω2×

1

4

=

1

8

ma2ω2 ........(iv)
Hence,

KE′

PE

=

3 8 ma2ω2

1 8 ma2ω2

=3:1