need help solving what has the red X Thanks A 470-g block connected to a light s

Question

need help solving what has the red X Thanks

A 470-g block connected to a light spring for which the force constant is 5.90 N/is free to oscillate on a frictionless, horizontal surface. The block is displaced 5.10 cm from equilibrium and released from rest as in the figure. (A) Find the period of its motion. (B) Determine the maximum speed of the block. (C) W is the maximum acceleration of the block? (D) Express the position, velocity, and acceleration as functions of time in SI units. (A) Find the period of its motion. Conceptualize study the figure and imagine the block moving back and forth in simple harmonic motion once it is released. Set up an experimental model in the vertical direction by hanging a heavy object such as a stapler from a strong rubber band. Categorize The block is modeled as a particle in simple harmonic motion. Analyze Use the equation to find the angular frequency of the block-spring system: omega = Squareroot k/m = Squareroot 5.90/470 times 10^-3 kg = 3.54 rad/s Use the equation to find the period of the system: T = 2 ppi/omega = 2 pi/3.54 rad/s = 1.774s. (B) Determine the maximum speed of the block. Use the equation to find v_max: V_max = omega A = (3.54 rad/s)(5.10 times 10^-2m) = .18054m/s (C) What is the maximum acceleration of the block? Use the equation to find a_max: a_max = omega^2 A = (3.54 rad/s)^2 (5.10 times 10^-2 m) = .63911 m/s^2 (D) Express the position, velocity, and acceleration as functions of time in SI units. Find the phase constant from the initial condition that x = A at t = 0: x(0) = A cos phi = A rightarrow phi = 0 Use the equation to write an expression for x(t). Use the following as necessary: t x = A cos(omega t + phi) = a cos (omega t) Use the equation to write an expression for v(t). V = - omega A sin (omega t + phi) = - omega sin(omega t) Use the following as necessary for a(t). Use the equation as necessary: t a = - omega^2 A cos (omega t + phi) = - omega^2 a cos (omega t)

Explanation / Answer

x = A*cos(wt + phi)

at time t = 0

x = A

A = A*cos(phi)

phi = 0

x(t) = (5.1*10^-2 m) cos(3.54rad/s*t)

x(t) = 0.051m cos(3.54t) <<<---------answer

v(t) = dx/dt

v(t) = -(18.1*10^-2 m/s)*sin(3.54rad/s*t)

v = -0.181m/s* sin(3.54rad/s*t) <<<---------answer

a(t) = dv/dt

a(t) = -(64.1*10^-2 m/s^2)*cos(3.54 rad/s*t)

a(t) = -0.641 m/s^2 *cos(3.54 rad/s*t) <<<<-------answer

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.