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
