A 0.400 kg block is attached to a spring with spring constant 500.0 N/m and oscillates horizontally with an amplitude of 2.66 cm on a frictionless table. The x-axis is defined such that when the block is at x = 0, the spring is at its equilibrium length. At time t = 0.100 s, the block is at x = -1.49 cm and is moving in the positive x direction.
a) What is the period of the block's oscillation?
b) What is the block's speed at t = 0.100 s? (optional: enter this value, in m/s, in the blank below)
c) What is the block’s maximum speed?
d) What is the block's acceleration at t = 0.100 s?
a) The period of the block's oscillation:
b) The speed of the block at t=0.1 s (at x=-1.49 cm) can be found from conservation of energy. The potential energy is maximum at x=2.66 cm, then it gradually converts into kinetic energy, which is maximum at x=0:
According to conservation of energy:
c) The maximum speed can be found from conservation of energy as well:
d) Find equation for velocity:
Comments
Leave a comment