Problem 2 An undamped spring-mass system has mass of 4.5 kg and a spring stiffness of 3500 N/m. It is excited by a harmonic (sinus) force having an amplitude Fo = 100 N and excitation frequency of 10 rad/s. The initial conditions are xo = 0.015 m and i o= 0.15 m/s. Answer to the following questions. Report the unit of measure and the equations that you used in all your answers. Required: 1. Determine the frequency ratio. 2. Determine the amplitude A of the forced response. 3. Determine the displacement of the system at time t = 2 s.
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- For Parts I and II, use the pendulum equation and solve to predict the length needed for a pendulum with a period of 1 s and 2 s respectively. Use a piece of string (or thread, dental floss, shoe lace, etc.) and a steel nut (or washer or something small but with enough mass to weigh down the string) to build each pendulum. Time each pendulum for 30 periods and then find the average time for one period. Remember, a period is the time to complete one cycle of motion, out and back. Tape each pendulum up in perhaps a doorway where it is stationary and has room to swing. Be precise with your measuring and timing. Show your work. Part I Given: T = 1.00 s l =? Part II Given: T = 2.00 s l =?DONT MIND THE BIG NUMBER ON THE RIGHT, IT IS JUST FOR NUMBERING. MAKE SURE IT IS CORRECT AND TYPEWRITTEN TO GET AN UPVOTE. NO UPVOTE IF IT IS HANDWRITTEN. THANK YOUDo number 2
- 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.The relationship between the length of a pendulum L and the time T for one complete oscillation can be determined from the data in the table to the right. a. Find the least squares line equation and graph it simultaneously with the data points, with L as the horizontal axis and T as the vertical axis. Does it seem to fit the data? b. Find the correlation coefficient and interpret it. Does it confirm your answer to part a? L (ft) T (sec) 1.0 1.13 1.5 1.36 2.0 1.57 2.5 1.76 3.0 1.92 3.5 2.08 4.0 2.22Item 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…