Question

An m = 5.2 kg box slides into a spring of spring constant k = 320 N/m (see figure below), compressing it 0.277 m. How long is the box in contact with the spring before it bounces off in the opposite direction? Round your answer to the second decimal place.

Answer 1

The time in which the box is in contact with the spring is 0.40 second.

How to calculate the time in contact?

The time in which the box is in contact with the spring is calculated by applying the following formula as shown below;

x = A cos(ωt)

where;

• x is the displacement
• A is the amplitude
• ω is the angular speed
• t is the time

The angular speed is calculated as follows;

ω = √ (k/m)

ω = √ (320 / 5.2)

ω = 7.85 rad/s

x = A cos(ωt)

-0.277 = 0.277 cos(7.85t)

cos(7.85t) = -1

7.85t = arc cos (-1)

7.85t = 3.14

t = 3.14 / 7.85

t = 0.40 s