The position of a point on a vibrating string is described (along a straight line) by the function
x(t)=4sin(2πt)m,0≤t≤4s.
Solve the following sub-questions with proper reasoning and working.
(a) Sketch the displacement–time graph of the motion for 0≤t≤4s. Mark clearly the point corresponding to t=1s.
(b) Write the equation of the straight line that is tangent to the curve at t=1s. Show the steps leading to your result.
(c) Using the tangent obtained in part (b), find the instantaneous speed of the point at t=1s.
(d) Determine the values of t (within the given interval) for which the instantaneous velocity of the point becomes zero. Explain the physical significance of these instants in the context of the motion.