400 g block, attached to the end of an ideal spring (horizontal) with force constant k=10 K/m, undergoes simple harmonic motion with a maximum displacement of .05 meter from the relaxed position. Neglect any air resistance or friction.
a. Estimate the amplitude of oscillations.
b. Calculate maximum speed of the block.
c. Evaluate magnitude of the maximum acceleration of the block.
d. Calculate angular frequency of the oscillations.
e. Find at which position the acceleration (magnitude) of the block is the maximum.
f. Find at which position the velocity (magnitude) of the block is the maximum.
g. How much time does it take the block to travel from a farthest position to the position three (quarter of a cycle).
h. Evaluate at which position the acceleration is zero?
i. Determine at which position the velocity is zero?
j. Compute the linear frequency of the oscillations?
k. Find the total mechanical energy of the block at the position four (full circle)
l. Define the explicit formula of displacement as a function of time.