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1. In a vibration experiment, a block of mass m is attached to a spring of stiffness k, and a dash pot with damping coefficient c. To start the experiment, the block is moved from the equilibrium position and then released from rest. The position of the block as a function of time is recorded at a frequency of5 Hz. The data points for 4

The goal here is to use the measured position data at different times, to evaluate the velocity andacceleration of the block as, v=\frac{d x}{d t} ; \quad a=\frac{d v}{d t} (a) Since the given data are discrete, introduce a notation involving index n to represent different time instances. For example, tn, represents time at the nh data point and n = 1, 2 , 3, .. Define your notation representing position, velocity, and acceleration at these discrete points. Compute the time interval (At) for the data (time-step). Is the time interval uniform? (b) Calculate the velocity and then the acceleration at time t = 5 and t = 6s using the central difference methods. Show all steps on paper (do manual calculations using the calculator).Present your results in a table indicating the velocity and accelerations at the two time instances. (c) Can one use central differencing to calculate velocity at t = 4 and t = 8s? Why or why not? If not, what differencing method can be used at t = 4s? And at t = 8s? (d) Calculate the velocity (calculator based) of the block at all data points within 4

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