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.

Some people modify cars to be much closer to the ground than when manufactured. Should they install stiffer springs? Explain your answer.

A physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the system for small angles of oscillation? For solid sphere Icm = 2/5 mr2. Also, why is the distance of the center of mass of the system from the point of oscillation 3R/2?

The position with time of an object is given byx(t)=Acos(ωt)  If the amplitude is 1.62 m, and the frequency is 1 Hz, what is the object's velocity at 2.3 seconds?

A .25kg harmonoc oscillator has a total mechanical energy of 4.0 J. If the oscillation amplitude is 20 cm. What is the angular speed, in rad/s?

A small sphere with mass m is attached to a massless rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side so that the rod is at an angle θ from the vertical, and released from rest. At this point, what is the linear acceleration of the sphere? Express your answer in terms of g, θ

A mathematical pendulum of mass 1.0 kg and length 1.0 m is moved by an angle 60° from the vertical axis and then let go. How fast does the wight move at the moment the rope encloses an angle of 30° with the vertical axis?

For a simple harmonic oscillator with x=Asinωt write down an expression for the magnitude of acceleration. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes).

A ball attached to a spring is raised 2 feet and released with an initial vertical velocity of 3 feet per second. The distance of the ball from its rest position after t seconds is given by d = 2 cos t + 3 sin t. Show that 2 cos t + 3 sin t = √13 cos(t - θ),where θ lies in quadrant I and tanθ =( 3/2). Use the identity to find the amplitude and the period of the ball’s motion.

A wheel of the F vehicle, developed for an experimental purpose, and a mechanism attached to it are shown in the figure. The speed of the center of mass of the wheel rolling without sliding is constant and ?=36??/??. A pin fixed on the wheel can give oscillating movement to the OA bar, which can rotate around the O point. In another slot above the OA bar, the DB control bar is moved back and forth via pin B. At the moment shown in the figure:a. Find the speed and acceleration vector of pin A.b. Find the angular velocity and angular acceleration vector of the OA bar.c. Find the acceleration of the DB control bar