A spring has a stiffness of 30 KN/m and supports a mass of 8 kg. The mass is pulled so that the spring t extends by amplitude of 10 mm and its released so that it produces linear oscillations .
(i) Determine the periodic time,circular frequency,and the natural frequency f.
(ii) Calculate the maximum velocity of the mass.(iii) Calculate the maximum acceleration of the mass.
The Attempt at a Solution
T = 1/f = (1 / 9.75) = 0.10260s
W= √ k / M w = √ 30000 / 8 = 61.24 rad/s
F = w / 2 π = 61.24 / (2π) = 9.75Hz
Displacenent . [/B]10 cos X (61.24 X 0.10260) = - 5.27 mm
Which equations do I use ? Velocity = ωx sin ωt Or max velocity = x cos ωt =0
Acceleration= ω^2 x sin ωt Or max acceleration= x cos ωt
If I am correct with displacement , it does not equal zero.Which is throwing me !