When a particular mass-spring system is started by stretching the spring 3 cm, one complete oscillation takes 4 seconds.

(a) If instead the initial stretch had been 5 cm, how long would it take for one complete oscillation?

Time for one oscillation = s

(b) If the mass were doubled, what would the period of the system be?

Period = s

A. 5.16 s.

B. 5.66 s.

Step-by-step explanation:

A.

For a simple harmonic motion,

T = 2pi (sqrt * (l/g))

Given:

L1 = 3 cm

T1 = 4 s

L2 = 5 cm

T2 = ?

4 = 2pi*sqrt (3/g)

g = 7.4

At, L2,

T2 = 2pi*sqrt (5/7.4)

= 5.16 s.

B.

M1 = M1

M2 = 2*M1

For a simple harmonic motion,

T = 2pi (sqrt * (m/k))

4 = 2pi (sqrt * (M1/k))

M1/k = 0.405

Inputting the above values,

T2 = 2pi (sqrt * (2*M1/k))

= 2pi (sqrt * (2 * 0.405))

= 5.66 s.