You are to complete Fig. 15-22 a so that it is a plot of velocity v versus time t for the spring–block oscillator that is shown in Fig. 15-22 b for t = 0. (a) In Fig. 15-22 a , at which lettered point or in what region between the points should the (vertical) v axis intersect the t axis? (For example, should it intersect at point A , or maybe in the region between points A and B? ) (b) If the block’s velocity is given by v = − v m sin(ω t + ϕ ), what is the value of ϕ ? Make it positive, and if you cannot specify the value (such as + π/ 2 rad), then give a range of values (such as between 0 π/ 2 and rad). Figure 15-22 Question 5.
You are to complete Fig. 15-22 a so that it is a plot of velocity v versus time t for the spring–block oscillator that is shown in Fig. 15-22 b for t = 0. (a) In Fig. 15-22 a , at which lettered point or in what region between the points should the (vertical) v axis intersect the t axis? (For example, should it intersect at point A , or maybe in the region between points A and B? ) (b) If the block’s velocity is given by v = − v m sin(ω t + ϕ ), what is the value of ϕ ? Make it positive, and if you cannot specify the value (such as + π/ 2 rad), then give a range of values (such as between 0 π/ 2 and rad). Figure 15-22 Question 5.
You are to complete Fig. 15-22a so that it is a plot of velocity v versus time t for the spring–block oscillator that is shown in Fig. 15-22b for t = 0. (a) In Fig. 15-22a, at which lettered point or in what region between the points should the (vertical) v axis intersect the t axis? (For example, should it intersect at point A, or maybe in the region between points A and B?) (b) If the block’s velocity is given by v = −vm sin(ωt + ϕ), what is the value of ϕ? Make it positive, and if you cannot specify the value (such as + π/2 rad), then give a range of values (such as between 0 π/2 and rad).
After a mass m is attached to a spring, the spring is stretched s units and hangs at rest at the equilibrium position as shown in Figure 1.3.17(b). Then the spring/mass system is set in motion, let x(t) denote the directed distance from the equilibrium point to the mass. As shown in Figure 1.3.17(c), assume that the downward direction is positive and that the motion is on a vertical straight line through the center of gravity of the mass and that the only forces acting on the system are the weight of the mass and the restoring force of the stretched spring. Use Hooke's law: the restoring force of a spring is proportional to its total elongation.
Determine a differential equation of the displacement x(t) at time t>0.
please answer as soon as possible :)
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression,
x = 3.00 cos(4t +(pi/6))
where x is in centimeters and t is in seconds.
(a) At t = 0, find the position of the piston.(b) At t = 0, find velocity of the piston.(c) At t = 0, find acceleration of the piston. (d) Find the period and amplitude of the motion.
A sphere of mass m=3.5 kg can move across a horizontal, frictionless surface. Attached to the sphere is an ideal spring with spring constant k=24 N/m. At time t=0the sphere is pulled aside from the equilibrium position, x=0, a distance d=12 cm in the positive direction and released from rest. After this time, the system oscillates between x=±d.
a. Determine the magnitude of the force, in newtons, required to initially displace the sphere d=12�=12 centimeters from equilibrium.
b. What is the sphere's distance from equilibrium, in meters, at time t=1�=1 second? c. Determine the frequency, in hertz, with which the spring–mass system oscillates after being released. d. Calculate the maximum speed, in meters per second, attained by the sphere. e. At what point in the motion does the sphere reach maximum speed? f. Calculate the magnitude of the maximum acceleration, in meters per second squared, experienced by the sphere.
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