Physics

Problem

Consider again a mass

m

attached to an ideal spring of force constant

k

executing simple harmonic motion on a frictionless horizontal surface. a. (i) Derive an expression for the time period

T

of the oscillation in terms of

m

and

k

. b. (ii) The same mass is now attached simultaneously to two identical springs, each of force constant

k

, connected in parallel between two fixed walls so that both springs act together on the mass. Derive the new time period

T_{\text{parallel}}

of oscillation. c. (iii) Compare

T

and

T_{\text{parallel}}

, and briefly explain the physical reason for the difference.