The point of the needle of a sewing machine moves in shm along the x-axis with a frequency of 2.5 hz. at t = 0 its position and velocity components are +1.1 cm and −15 cm/s, respectively.
a) find the acceleration component of the needle at t = 0.
b) write equations giving the position, velocity, and acceleration components of the point as a function of time.
2. this procedure has been used to "weigh" astronauts in space: a 42.5-kg chair is attached to a spring and allowed to oscillate. when it is empty, the chair takes 1.30 s to make one complete vibration. but with an astronaut sitting in it, with her feet off the floor, the chair takes 2.54 s for one cycle. what is the mass of the astronaut?
3. a 175-g glider on a horizontal, frictionless air track is attached to a fixed ideal spring with force constant 155 n/m. at the instant you make measurements on the glider, it is moving at 0.815 m/s and is 3.00 cm from its equilibrium point. use energy conservation to find
a) the amplitude of the motion and
b) the maximum speed of the glider.
c) what is the angular frequency of the oscillations?