Suppose that the mass which produced a period of 1.00 seconds was 200.0 grams. W

Question

Suppose that the mass which produced a period of 1.00 seconds was 200.0 grams. What was the spring's constant ? The spring's constant was N/m. what is the mum acceleration of the above mass (period 1.00 seconds and mass 200.0 grams) if the initial displacement is 5.00 cm and the mass is released from rest? The mass's minimum acceleration is m/s^2. (Bonus) What is the maximum acceleration of the above mass (period 1.00 seconds and mass 200.0 grams) if the initial displacement is 5.00 cm and the mass is released from rest? The mass's maximum acceleration is m/s^2. (Bonus) What is the maximum speed of the above mass (period 1.00 seconds and mass 200.0 grams) if the initial displacement is 5.00 cm and the mass is released from rest? The mass's maximum speed is m/s.

Explanation / Answer

A)

time period = 1 s

mass , m = 200 gm

m = 0.2 Kg

let the spring constant is k

T = 2pi * sqrt(m/k)

1 = 2pi * sqrt(0.2/k)

solving for k

k = 7.89 N/m

the spring constant is 7.89 N/m

part B)

the minimum acceleration is at the equilibrium position

minimum acceleration = 0 m/s^2

part C)

for the maximum acceleration

maximum acceleration = (2pi/T)^2 * A

maximum acceleration = (2pi/1)^2 * 0.05 m/s^2

maximum acceleration = 1.973 m/s^2

the maximum acceleration is 1.973 m/s^2

part D)

maximum speed = (2pi/T) * A

maximum speed = (2pi/1) * 0.05

maximum speed = 0.314 m/s

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