A mass m is attached to a spring with spring constant k on a frictionless table. We stretch and release it a distance to away from the resting position. (a) Sketch the position, velocity, and acceleration plots (time on x-axis). (b) What is the period if: (i) the mass is doubled, (ii) or the spring constant is quadrupled, and (iii) or we double ro but the mass and spring constant remain unchanged? (c) On one plot, sketch the total energy, kinetic energy, and elastic energy with time on the xr-axis. (d) When the mass is at the position -ro/3, what is the velocity? (e) At what distance will the speed of the mass be half of its maximum speed?

Using the spring force, F = -kx, calculate: a) The work done by an external force stretching the spring a distance L away from the equilibrium length. b) At a stretch length L, how much potential energy is stored in the spring? If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity c) of the mass? d) At what x coordinate does this maximum velocity occur?

A clock is constructed so that it keeps perfect time when its simple pendulum has a period of exactly 1.000 s. The pendulum bob has length L = 0.2483 m and, instead of keeping perfect time, the clock runs slow by 1.506 minutes per day. (a) What is the free-fall acceleration (in m/s2) at the clock's location? (Give your answer to at least 3 decimal places.)  ?m/s2 (b) What length of pendulum bob (in m) is required for the clock to keep perfect time? (Give your answer to at least 4 decimal places.)  ?m