Question

A 50-gram mass is attached to a vertical spring; the spring stretches 8.0 cm. Determine the stiffness of the spring. If it is now stretched an additional 2.0 cm, determine its period and frequency of oscillation.

A 50-gram mass is attached to a vertical spring; the spring stretches 8.0 cm. Determine the stiffness of the spring. If it is now stretched an additional 2.0 cm, determine its period and frequency of oscillation.

Answer 1

Mass ,m =50 gm = 0.05kg.

Weight ,F= mg = 0.05×9.8 N = 0.49 N , where g= acceleration due to gravity= 9.8m/s^2

Spring stretches ,x= 8.0cm = 0.08m

So , stiffness of the spring , K=F/x = 0.49/0.08 N/m = 6.125 N/m

So,stiffness constant , K = 6.125 N/m

Now , period of oscillation ,

putting the values we get time period of oscillation ,

So , time period = 0.567 S

Frequency f = 1/T = 1/0.567 = 1.761 Hz

Answer: stiffness constant =6.125 N/m

Time period= 0.567 S

Frequency = 1.761 Hz

Thank you.