A spring-mass system shown in the diagrambelow is free to oscillate in the verticaldirection.I+sunstretchedx< 0x- 0equilibriumpositionmg - ks - 0x>0motionThe position (x) of the spring is positive whenthe spring is below the equilibrium position. Ifthe block is displaced from its equilibriumposition by a distance x, show that itsequation of motion is given by:KmWhy is it that the equation of motion does notinclude the force of gravity?In which direction does the velocity of themoving mass have a positive value?

We here, apply Newton's second law of motion and get the equation of motion.

Answered: A spring-mass system shown in the…

Similar questions

Find the equation of simple harmonic motion for a spring mass system where the mass is hanging off the ceiling with the help of a spring if the initial displacement is 1 ft above equilibrium with initial upward velocity of 2 ft/s. Assume w=1. Write in form y=Asin(x+b). Solve for A, x, and b.
A small piece of rounded stone perforated for threading is sliding on a wire which is hanging freely in the shape of a cosh function. Assume the stone moves with no friction. For very small displacements in x, what is the frequency of oscillation? You may use for the height of the wire and thus the height of the stone as a function of x the Taylor series expansion of cosh. G(x) =1 + x2/2 + x4/24 + ...
Michelle pulls a slinky a distance of 13 inches from its equilibrium position and then releases it. The time for one oscillation is 2 seconds. Step 2 of 2 : Find the function in terms of t for the displacement of the slinky. Assume that the slinky is at its maximum displacement at t=0. Also assume that the function includes no horizontal or vertical shifts.
A stiff spring k = 666 N/m has be attached to the floor vertically. A mass of 6.66 kg is placed on top of the spring as shown below and it finds a new equilibrium point. If the block is pressed downward and released it oscillates. If the compression is too big, however, the block will lose contact with the spring at the maximum vertical extension. Draw a free body diagram and find that extension at which the block loses contact with the spring.
You will fire the spring gun 3 times from the first detent and measure the change in height of the (pendulum + ball) for each shot. Write the equation for the change in height of the first shot.
A spring with a spring constant of 200 N/m with a 5 kg mass attached to it has the following position function. ?(?) = 5 cos (0.3 ?) (The 5 has units of m and the time is in seconds.) What is the frequency of oscillation for the mass? What is the period of oscillation?
Item 1 Learning Goal: To understand the application of the general harmonic equation to the kinematics of a spring oscillator. One end of a spring with spring constant k is attached to the wall. The other end is attached to a block of mass m. The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be x = 0. The length of the relaxed spring is L. (Figure 1) The block is slowly pulled from its equilibrium position to some position init> 0 along the x axis. At time t = 0, the block is released with zero initial velocity. The goal is to determine the position of the block (t) as a function of time in terms of w and init It is known that a general solution for the displacement from equilibrium of a harmonic oscillator is x(t) = C cos (wt) + S sin (wt), where C, S, and w are constants. (Figure 2) Your task, therefore, is to determine the values of C and S in terms of w and init Figure 1 of 3 L Xinit win x = 0 Part A Using the…
Please help solve for v in (m/s)
A student plans to measure the Period of oscillation. That student should: A) Start the clock at the equilibrium position and end it at either Amplitude. B) Start the clock at the Amplitude and end it at the opposite Amplitude. C) Start the clock at the equilibrium position and end it at the equilibrium position. D) Start the clock at the Amplitude and end it at the same Amplitude.