The motion of a particle is given by x = A sin3(ωt). (a) Enter an expression...

The motion of a particle is given by x = A sin³(ωt).

(a) Enter an expression for the amplitude of the particle's motion.

(b) Enter an expression for the particle's velocity, v.

(c) Enter an expression for the particle's acceleration, a.

Expert Solution

genius_generous answered 1 year ago

The x and y coordinates of a particle in motion as functionsof time t, are given...

The x and y coordinates of a particle in motion as functionsof time t, are given by: x=5t^2-5t+6 y=3t^3-3t^2-12t-4 At the instant the x-component of velocity is equal to zero,the y component of the acceleration is closest to: A. 12 B. -24 C. -15 D. -1.5 E. 3.0

particle is in simple harmonic motion along the x axis. The amplitude of the motion is...

particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = −1 2x1, the kinetic and potential energies are: A. K = 5 J and U = 3J B. K = 5 J and U...

The equation x(t) = A sin(ωt + φ) describes the simple harmonic motion of a block...

The equation x(t) = A sin(ωt + φ) describes the simple harmonic motion of a block attached to a spring with spring constant k = 20 N/m. At t = 0 s, x = 0.5 m and the block is at rest. a (5 points) After 0.5 s, the potential energy stored in the spring first reaches zero and the velocity of the block is in the negative x direction. What is the period of the oscillation? b (5 points)...

A particle executes simple harmonic motion, such that at a given time, it is at ?A/3...

A particle executes simple harmonic motion, such that at a given time, it is at ?A/3 moving in towards equilibrium. 0.7seconds later, it is at x=0.9A moving towards equilibrium. Find the angular frequency of the particle, if it passes through equilibrium once between the two occurrences. Repeat the above, with the particle passing through equilibrium 5times between the two occurrences.

1.The position of a particle in rectilinear motion is given by s (t) = 3sen (t)...

1.The position of a particle in rectilinear motion is given by s (t) = 3sen (t) + t ^ 2 + 7. Find the speed of the particle when its acceleration is zero. 2.Approximate the area bounded by the graph of y = -x ^ 2 + x + 2, the y-axis, the x-axis, and the line x = 2. a) Using Reimmann sums with 4 subintervals and the extreme points on the right. b) Using Reimmann sums with 4...

The motion of a 16.1 lb. particle is given by: r(ϴ) = (5sin 2ϴ) ft, with...

The motion of a 16.1 lb. particle is given by: r(ϴ) = (5sin 2ϴ) ft, with ϴ(t) = πt/4 rad, and t in seconds. Determine the magnitudes of the particle’s position, velocity, acceleration, linear momentum, net force, and T (K.E.) at t = 2 s.

The position of a particle moving along the x axis is given in centimeters by x...

The position of a particle moving along the x axis is given in centimeters by x = 9.72 + 1.85 t3, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t = 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is...

The position of a particle moving along an x axis is given by x = 12.0t2...

The position of a particle moving along an x axis is given by x = 12.0t2 - 4.00t3, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 5.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at...

The potential of a particle is given as V (x) = -Vδ (x), with V being...

The potential of a particle is given as V (x) = -Vδ (x), with V being a positive number. Find the wave function and energy of the bounded states of this particle.

The position of a particle moving along an x axis is given by x = 16.0t2...

The position of a particle moving along an x axis is given by x = 16.0t2 - 6.00t3, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t = 3.00 s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at...

Question