Amass m = 1.1 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. the spring has spring constant k = 55 n/m and negligible mass. the mass undergoes simple harmonic motion when placed in vertical motion, with its position given as a function of time by y(t) = a cos(ωt – φ), with the positive y-axis pointing upward. at time t = 0 the mass is observed to be passing through its equilibrium height with an upward speed of v0 = 4.6 m/s.
1. find the angular frequency of the oscillation, in radians per second.
2. find the smallest positive value of phi. in radians. calculate the value of a. in meters.