Mass on vertical spring: frequency, max velocity, acceleration, and equations

[Kev1n]

1. If anyone is able to cast an eye over my work and comment would be appreciated. Q. A mass attached to the lower end of a vertical spring causes the spring to extend by 25mm to its equilibrium position. The mass is then displaced a further 20mm and released. A trace vibration and time measurement are taken. Thes show thet the displacement from the equilibrium position is 19.2mm when the time is 0.05s. A. Caluclate the expected frequency of vibration, B. Max acceleration of the mass, C. Max velocity of the mass, D. Write the expression for the displacement of the mass as as function of time, E.Write the expression for the velocity as function of time, F. Write the expression for the acceleration of the mass as a function of time



2. F= 1/T, T=1/F, A=DV/DT, V=DX/DT



3. A. F=1/T, 1/0.05 = 20hz
B. a= DV/DT = 0.384/0.05 = 0.768ms
C. V=DX/DT = 0.0192/0.05 = 0.384ms
D. X(t) = A*Cos(tSqr(k/m)
E Unsure
F unsure
Any comments appreciated

 

[kuruman]

A. What makes you think that the period is 0.05 s? What is the definition of period?
B. Where did 0.384 come from? Why do you think that dividing it by 0.05 (what you call the period) will give you the maximum acceleration?

The fact that the spring extends by 25 mm when you attach the mass is important. Draw a free body diagram of the suspended mass at rest and use it to find an expression relating the mass, the spring constant, the acceleration of gravity and the amount by which the spring stretches. This should help you find the frequency.