Question

A mass is oscillating up and down at the end of a spring similar to Activity 2. A graph of displacement as a function of time is shown where up is the positive direction O-4 time (s) 1. What is the period of this motion? Explain your reasoning. 2. At which point or points is the acceleration positive? Explain your reasoning. 3. At which point or points does the mass have a zero velocity but nonzero net force? Explain your reasoning. 4. At which point or points is the net force on the mass equal to zero? Explain your reasoning 5. At which point or points are the acceleration, velocity, and displacement all positive? Explain your reasoning.

Answer 1

Period is the time to complete one oscillation, here it is two second from the graph, T = 2 sec Equation of motion from the graph x = A sin (wt) y = wA cos (wt) a = -w^2 A sin (wT) = -w^2 x a alpha - x Therefore acceleration will be positive, if displacement in negative A points C and D acceleration is positive Velocity is the slope of position vs time, it is zero at points A and D. Also Vertical-bar x Vertical-bar is maximum at these parts, therefore at points A and D velocity is zero but nonzero force points A and D Acceleration is zero, if x = 0 Point E If displacement is positive, acceleration will be negative and velocity positive. Therefore at no points all will be positive. No points