A particle with mass 1.53 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.987 m and a duration of 121 s for 78 cycles of oscillation. Find the frequency (f), the speed at the equilibrium position (vmax), the spring constant (k), the potential energy at an endpoint (Umax), the potential energy when the particle is located 60.5% of the amplitude away from the equiliibrium position (U), and the kinetic energy (K), and the speed (v), at the same position.

Afaulty model rocket moves in the xy-plane (the positive y direction is vertically upward). the rocket's acceleration has components ax(t) = ? t2 and ay(t) = ? ? ? t, where ? = 2.50 m/s4 , ? = 9.00 m/s2 , and ? = 1.40 m/s3 . at t = 0 the rocket is at the origin and has velocity ~v0 = v0x ? i + v0y ? j with v0x = 1.00 m/s and v0y = 7.00 m/s. (a) calculate the velocity and position vectors as functions of time. (b) what is the maximum height reached by the rocket? (c) sketch the path of the rocket. (d) what is the horizontal displacement of the rocket when it returns to y = 0?