Question

A particle executes simple harmonic motion under the restoring force provided by a spring. The time period is T. If the spring is divided into two equal parts and one part is used to continue the simple harmonic motion, the time period will
(a) remain T
(b) become 2T
(c) become T/2
(d) become T/√2

Answer 1

Answer ⇒ T' = T/√2.  Option (d).

Explanation ⇒ Using the formula,

Time Period of Spring = 2π √(m/k)

m is the mass of the spring and k is the spring constant.

Now, if the spring is divided into two equal parts, then the new spring constant will be 2k for both the spring.

Therefore, New time period will be,

T' = 2π √(m/2k)

∴ T'/T = 1/√2

T' = T/√2

Therefore, Option (d). is correct.

Hope it helps .

Hope it helps.