Simple Harmonic Motion

Step 1: Find Spring Constant (k)
The spring stretches by 0.2 m when a 0.5 kg mass hangs from it.
This means the force from the weight (m1g) equals the force from the spring (kx) :
kx=m1g
So,
k=‌

m1g

x

=‌

0.5×10

0.2

=25N∕m
Step 2: Use the New Mass
The new hanging mass is m2=0.25kg.
Step 3: Find the New Time Period ( T )
The time period of a mass-spring system is:
T=2π√‌

m2

k

Substitute the values:
T=2π√‌

0.25

25

T=2π√0.01
T=2π×0.1=0.2πs
Step 4: Calculate the Value Using π≈3.14 :
T=0.2×3.14=0.628s