Question

A mass spring system it in in simple harmonic motion in the horizontal direction if the mass is 0. 25 kg whose spring constant is 12 Newton per meter and the amplitude is 15 cm what's the speed at a half amplitude position

Answer 1

To find the speed of the mass at a half-amplitude position in simple harmonic motion, we can use the following formula for the speed of an object undergoing simple harmonic motion:

v = ω * A

where:
v = speed of the mass at the given position
ω (omega) = angular frequency of the motion
A = amplitude of the motion

The angular frequency (ω) of the motion can be calculated using the formula:

ω = √(k / m)

where:
k = spring constant
m = mass

Given:
m = 0.25 kg
k = 12 N/m
A = 15 cm = 0.15 m

Let's calculate the angular frequency first:

ω = √(12 N/m / 0.25 kg)
ω = √(48 N/kg)
ω = 6 rad/s

Now, we can calculate the speed at a half-amplitude position:

v = ω * A
v = 6 rad/s * 0.15 m
v = 0.9 m/s

So, the speed of the mass at a half-amplitude position is 0.9 meters per second (m/s).