One equation modeling the displacement of a spring in damped harmonic motion isd=A e" sin 2rt. Find the times when the spring is at its equilibrium point, i.e. when d=0.

Suppose a teacher is riding a Ferris wheel. The maximum height they attain is 30 m and theminimum height is 6 m. The time it takes to make one full rotation is about 5 minutes. Determine:a/ The periodb/ The amplitudec/ A possible equation that models this situation, if the time starts at the minimum height.

A 6.13-kg object oscillates back and forth at the end of a spring whose spring constant is 55.4 N/m. An observer is traveling at a speed of 2.80 x 108 m/s relative to the fixed end of the spring. What does this observer measure for the period of oscillation? Number i Units

H2. A simple pendulum has a particle of mass m at the end of a light rod of length 1. The other end of the rod is attached to a fixed point O, at the origin of polar coordinates (r, 0). The particle is at position (r, 0) with 0 = 0 corresponding to the particle being vertically below O. (a) Use the formulae for acceleration in polar coordinates, a = ( − rġ²) + (2rė + rö)ê to show that cos 0 + A, 8 T = mg cos 0 + mlė², where T' is the tension in the rod. Use the relation (0²) = 200 to deduce that 2g ². = 1 and 0 == sin sin 0, (1) where A is a constant. If the particle is instantaneously at rest ( = 0) when the rod is horizontal, find and T when the rod is vertical. How does the tension in the vertical position (which is also the maximal tension) depend on the rod's length /? (b) Assume the particle is subject to linear air resistance av. Use the expression of the velocity in polar coordinates v=rf+rẻÔ (2) together with (1) to write the equations of motion in polar coordinates. Show…

A 0.75-kg mass oscillates according to the equation x(t)=0.85 cos(7.5t), where the position x(t) is measured in meters. What is the period, in seconds, of this mass?  At what point during the cycle is the mass moving at its maximum speed?