Step 1: Calculation of spring constant of wire
Young's modulus of wire,
Y=‌=‌×‌Due to elasticity of the wire, it behaves as equivalent spring
(K‌spring ‌=F∕∆x). Hence, Spring constant for Wire,
KW=‌=Y‌Step 2: Calculation of Equivalent spring constant
Let a force
F be applied to the end of the spring.
The wire will extend.
Total extension
∆S=x‌wire ‌+x‌spring ‌=‌+‌But
FS=Fw‌‌ (By Newton's, third Law, Both will apply equal and opposite forces at their joint A)
∴∆S=Fw(‌+‌) So, Equivalent spring constant
(Keq) is given by:
Keq=‌=‌=‌Keq=‌=‌=‌Step 3: Calculation of Time period
Angular frequency
ω for spring block system is given by:
ω=√‌=√‌∴‌ Time period, ‌T=‌=2π√‌