Oscillations Part 1

Given, mass of particle, m = 1kg
Spring constant, k=100Nm−1
Let time period is T.
Kinetic energy (KE) = Potential energy (PE) = E
Amplitude = A
Angular velocity = ω
Wave displacement = x
KE in SHM = PE in SHM
⇒

1

2

mω2(A2−x2)=

1

2

kx2
⇒mω2(A2−x2)=kx2 ...(i)
Since, force, F=mω2x=kx
⇒k=mω2
Substituting the value in Eq. (i), we get
⇒mω2(A2−x2)=mω2x2
⇒A2−x2=x2
⇒A2=2x2
⇒x=

A

√2

Since, wave displacement, x=A‌sin‌ω‌t
⇒

A

√2

=A‌sin‌ω‌t
⇒sin(

π

4

)=sin‌ω‌t
⇒ωt=

π

4

⇒

2π

T

.t=

π

4

⇒t=

T

8

Comparing the given value in the question i.e.

T

x

, the value of x = 8