Question

A first course in differential equations: HW question chapter 5.1 Simple Harmonic Motion

Please solve Problem 21 all parts, thanks

21. A 64-lb weight attached to the end of a spring stretches it 0.32 ft. From a position 8 in. above the equilibrium position the weight is given a down ward velocitv of 5 ft/s. (a) Find the equation of motion. (b) What are the amplitude and period of motion? 191 SECTION 5.1 Simple Harmonic Motion (c) How many complete vibrations will the weight have completed at the end of 3T seconds? (d) At what time does the weight pass through the equilibrium position heading downward for the second time? (e) At what time does the weight attain its extreme displacement on either side of the equilibrium position? (f) What is the position of the weight at t - 3 seconds? (g) What is the instantaneous velocity at t-3 seconds? (h) What is the acceleration at t-3 seconds? (i) What is the instantaneous velocity at the times when the weight passes through the equilibrium position? 191 SECTION 5.1 Simple Harmonic Motion (c) How many complete vibrations will the weight have completed at the end of 3T seconds? (d) At what time does the weight pass through the equilibrium position heading downward for the second time? (e) At what time does the weight attain its extreme displacement on either side of the equilibrium position? (f) What is the position of the weight at t-3 seconds? (g) What is the instantaneous velocity at t-3 seconds? (h) What is the acceleration at t - 3 seconds? (i) What is the instantaneous velocity at the times when the weight passes through the equilibrium position? (j) At what times is the weight 5 in. below the equilibrium position? (k) At what times is the weight 5 in. below the equilibrium position head- ing in the upward direction?

Answer 1

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