Question

A mass m is suspended from a spring of force constant k and another identical spring is fixed to the floor as shown. The time period of small oscillations is:

• A. 2π√((m)/(k))
• B. π√((m)/(k))+π√((m)/(2k))
• C. π√((m)/(3k/2))
• D. π√((m)/(k))+π√((m)/(2k))

Hint:

Springs in series reduce effective stiffness.

Answer 1

The Correct Option is D

Step 1: Effective spring constant.
Series combination: kₑq=(k)/(2)
Step 2: Time period.
T=2π√mkₑq