Write the vector expression for the acceleration a of the mass center G of the simple pendulum in both n-t and x-y coordinates for the instant when 8 = 58° if 0 = 1.84 rad/sec and 0 = 4.145 rad/sec². Answers: a = ( i a = (i 4.3' en + i i+ i et) ft/sec² j) ft/sec²

How do I summarize the two vectors shown?

Suppose that a simple pendulum consists of a small 67 g bob at the end of a cord of negligible mass. If the angle between the cord and the vertical is given by 0 = (0.063 rad) cos[(9.0 rad/s) t + ø], what are (a) the pendulum's length and (b) its maximum kinetic energy? (a) Number i 0.00000499 Units (b) Number i 0.000000269 Units ☐

You have a spring witk k+388 N/m When no extrenal forceis applied on it, the length of the spring is 4.5 cm When you exert F+ 8.5 N of force to stretch this spring,what is the length of the stretched spring in the unit of cm?

There are more than 300 species of hummingbirds in the world and about 10 species regularly breed in the United States. One of which is the Ruby-throated Hmmingbird who can flap its wings with an angular speed of 332 rad/s. Calculate the period of its flapping motion.

A pendulum's angular position is given by ?= 0.0340 cos (?t), where ? is in radians and ? = 6.23 rad/s.  Find the period (in s) and length (in m) of the pendulum.

A conical pendulum has length l and the angle made by the string with vertical is e = 35° . The mass of the object is m=124 g. If the speed of the object is v=3.9m/s find the length of the string. Take g=10Om/s2. Round your answer to one decimal place.

The figure blow shows the kinetic energy of a simple pendulum versus its angle θ from the vertical.  Note the energy units are in milli-joules.  The vertical axis is set by Ks=4mJ and the mass of the pendulum bob is 0.200 kg.  Determine the length of the pendulum in meters.  Use g = 9.8 N/kg.

MärkxsfH) Problem 1: A mass of 20 grams stretches a spring by 10/169 meters. (a) Find the spring constant k, the angular frequency w, as well as the period T and frequency f of free undamped motion for this spring-mass system. (b) Find the general solution x(t) of the DE for the free spring-mass system. (c) Suppose that an exterior force of F(t) = 2.5 sin(12t) in Newtons acts on the spring-mass system. Find the equation of motion (the solution x(t)) of the system if the mass initially is at rest in its equilibrium position.