A horizontal mass-spring system is in SHM. The mass is 0.25kg, the spring constant is 15N/m, and the amplitude is 20cm. a) What is the maximum speed of the mass and where does it occur? b) What is its speed at the 1/2 amplitude position of its motion?

maximum speed = 1.55 m/s

speed is 0.775 m/s

Explanation:

given data

mass m = 0.25 kg

spring constant k = 15 N/m

amplitude A = 20 cm = 0.2 m

to find out

maximum speed and speed at the 1/2 amplitude

solution

we know formula for maximum speed that is

maximum speed = amplitude * √ (k/mass)

put all value

maximum speed = 0.2 * √ (15/0.25)

maximum speed = 1.55 m/s

and

at the 1/2 amplitude

we apply here conservation of energy that is

1/2 * m*v² = 1/2 * k*x²

here we know x = A/2 that is 20 / 2 = 10 cm = 0.1 m

so

0.25 v² = 15 * 0.1²

v² = 0.600625

v = 0.775

so speed is 0.775 m/s