A 0.200 kg block is attached to a horizontal spring of force constant 8.0 N·m on a…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A 0.200 kg block is attached to a horizontal spring of force constant 8.0 N·m−1 on a friction-less surface. At t=0 the block is 0.050 m to the left of equilibrium and moving rightward with a speed of 0.30 m·s−1.
Respond to each part below.
(1) Calculate the angular frequency of the block’s oscillation.
(2) Using the given initial conditions, determine both the amplitude and the phase constant, then write a complete expression for the block’s displacement x(t).
(3) Find the earliest positive time at which the block passes through the equilibrium position while moving leftward.
(4) Determine the acceleration of the block at the instant found in part (c).
(5) Sketch qualitative graphs of x(t), v(t), and a(t) for the first two full periods, labelling key points such as maxima, minima, and zeros.