Could you please do 8,9, and 10 out of these questions please?


A 32 pound weight is attached to the lower end of a coiled spring suspended from the ceiling. The...
A 16-lb weight is attached to the lower end of a coil spring suspended from the ceiling and having a spring constant of 5 lb/ft. The resistance in the spring-mass system is numerically equal to the instantaneous velocity. At t=0 the weight is set in motion from a position 1 ft below its equilibrium position by giving it an upward velocity of 1 ft/sec. Write an initial value problem that models the given situation. Write the differential equation for the...
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...
(1 point) A weight is suspended from the ceiling by a spring. Let d be the distance in centimeters from the ceiling to the weight. When the weight is motionless, d 13cm. If the weight is disturbed, it begins to bob up and down, or oscillate. Then d is a periodic function of t, the time in seconds, so d-0.Consider the graph of d ) below, which represents the distance of the weight from the celling at time 2018/HW 10-Section...
(1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 3 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that this means...
(1 point) A steel ball weighing 128 pounds is suspended from a spring This stretches the spring 13 feet The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second) Suppose that after t seconds the ball is y feet below its rest position Find y in terms of t. (Note that this...
145 (1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128 feet The ball is started in motion from the equilibrium position with a downward velocity of 7 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that...
2) A 2-pound weight attached to the end of a spring stretches it 6 inches. At t= 0 and from a position 8 inches below the equilibrium position the weight is given a upward velocity of 3/4 ft/s. a) Find the equation of motion. b) What are the amplitude and period of motion? c) How many complete vibrations will the weight have completed at the end of 6t? d) What is the position of the weight at t=5s with respect...
(1 point) A steel ball weighing 128 pounds is suspended from a spring. This stretches the spring 128 257 feet. The ball is started in motion from the equilibrium position with a downward velocity of 3 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that...
A mass weighing 32 pounds is attached to the lower end of a coil spring. It stretches the spring by 1 foot and comes to rest at equilibrium position. At time t = 0, the mass is pulled downward 1 foot, and released. Suppose the damping is equivalent to 8x' pounds and no external forces are present. Find the displacement of the mass at time t, and write your final answer in phase-amplitude form.
A mass weighing 12 pounds stretches a spring 2 feet. The mass is initially released from a point 1 foot below the equilibrium position with an upward velocity of 4 ft/s. (Use g 32 ft/s for the acceleration due to gravity.) (a) Find the equation of motion x(t) (b) what are the amplitude, period, and frequency of the simple harmonic motion? amplitude1.118 ft period frequency cycles/s (c) At what times does the mass return to the point 1 foot below...