11. A mass weighing 64 pounds stretches a spring mass is initially released from a point 8 inches above th equilibrium position with a downward velocity of 5 ft/s. (a) Find the equation of motion. (b) What are the amplitude and period of motion? (c) How many complete cycles will the mass have complete at the end of 37 seconds? (d) At what time does the mass pass through the equilibriur position heading downward for the second time? (e) At what time does the mass attain its extreme displace ment on either side of the equilibrium position? (f) What is the position of the mass at t 3 s? (g) What is the instantaneous velocity at / = 3 s? (h) What is the acceleration at t = 3 s?
11. A mass weighing 64 pounds stretches a spring mass is initially released from a point 8 inches above th equilibrium position with a downward velocity of 5 ft/s. (a) Find the equation of motion. (b) What are the amplitude and period of motion? (c) How many complete cycles will the mass have complete at the end of 37 seconds? (d) At what time does the mass pass through the equilibriur position heading downward for the second time? (e) At what time does the mass attain its extreme displace ment on either side of the equilibrium position? (f) What is the position of the mass at t 3 s? (g) What is the instantaneous velocity at / = 3 s? (h) What is the acceleration at t = 3 s?
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Transcribed Image Text:11. A mass weighing 64 pounds stretches a spring 0.32 foot. The
mass is initially released from a point 8 inches above the
equilibrium position with a downward velocity of 5 ft/s.
(a) Find the equation of motion.
(b) What are the amplitude and period of motion?
(c) How many complete cycles will the mass have completec
at the end of 37 seconds?
(d) At what time does the mass pass through the equilibrium
position heading downward for the second time?
(e) At what time does the mass attain its extreme displace
ment on either side of the equilibrium position?
(f) What is the position of the mass att = 3 s?
(g) What is the instantaneous velocity at / = 3 s?
(h) What is the acceleration at i = 3 s?
(i) What is the instantaneous velocity at the times when the
mass passes through the equilibrium position?
(j) At what times is the mass 5 inches below the equilibrium
position?
(k) At what times is the mass 5 inches below the equilibriur
position heading in the upward direction?
12. A mass of 1 slug is suspended from a spring whose sprin
constant is 9 lb/ft. The mass is initially released from a poir
1 foot above the equilibrium position with an upward velocit
of V3 ft/s. Find the times for which the mass is heading dowr
ward at a velocity of 3 ft/s.
13. A mass weighing 20 pounds stretches one spring 6 inches an
another spring 2 inches. The springs are attached to a commo
rigid support and then to a metal plate of negligible mass a
shown in Figure 3.8.5; the mass is attached to the center c
the plate in the double-spring arrangement. Determine th
effective spring constant of this system. Find the equation c
motion if the mass is initially released from the equilibriur
position with a downward velocity of 2 ft/s.
14. A certain weight stretches one spring foot and anothe
spring foot. The two springs are attached in parallel to
common rigid support in a mannor i
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