A 0.420-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 11.4 cm. (Assume the position of the object is at the origin at t = 0.) (a) Calculate the maximum value of its speed. 0.47 x Have you calculated the angular velocity? You almost always need this quantity for problems involving simple harmonic motion. cm/s (b) Calculate the maximum value of its aceleration. | cm/s² (c) Calculate the value of its speed when the object is 9.40 cm from the equilibrium position. cm/s (d) Calculate the value of its acceleration when the object is 9.40 cm from the equilibrium position. cm/s2 (e) Calculate the time interval required for the object to move from x = 0 to x = 3.40 cm.

A peg on a turntable moves with a constant tangential speed of 0.67 m/s in a circle of radius 0.26m. The peg casts a shadow on a wall. Find the following quantities related to the motion of the shadow.1) Find the period. Express your answer using two significant figures. T=(?)s2) Find the amplitude. A=(?)m3) Find the Max Speed Vmax= (?) m/s4) Find the maximum magnitude of the acceleration. aMax=(?)m/s^2

In the figure, a solid cylinder attached to a horizontal spring (k = 4.70 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.170 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) If the cylinder has mass M = 9.30 kg, find the period of the simple harmonic motion that the cylinder's center of mass executes. (Hint: Find the time derivative of the total mechanical energy.) M (a) Number Units (b) Number Inits (c) Number Units

A particle undergoes simple harmonic motion with angular velocity of 3.0 rad/s and amplitude of 0.5 m. It starts with maximum forward displacement at time t = 0. Find the velocity at time t = 2.0 s

A 50.0 g mass is attached to a horizontal spring with a spring constant of 15.0 N/m and released from rest with an amplitude of 30.0 cm. What is the velocity of the mass when it is halfway to the equilibrium position if the surface is frictionless?m/s

In the figure, a solid cylinder attached to a horizontal spring (k = 5.80 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.290 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) If the cylinder has mass M = 6.20 kg, find the period of the simple harmonic motion that the cylinder's center of mass executes. (Hint: Find the time derivative of the total mechanical energy.) M · k oooooo (a) Number i 0. (b) Number i (c) Number i O. Units Units Units

You have made a physical pendulum by swinging a rod of mass M = 1.08 kg and length L = 1.45 meters around its end. The mass of the rod is distributed uniformly along its length. We will assume that the amplitude of the swing is max = 19.34 degrees. Solid Rod Swings in Simple Harmonic Motion ^ 0=-0, max 0=+0₁ max Determine all the following: The FORMULA for the moment of inertia of your rod, I = The distance from the pivot point to the Center-Of-Mass, d = The angular frequency of the pendulum, w = The amplitude of the motion in radians, max = radians The angular velocity when 0 = 64% of full swing, w(0 = 0.64 0max): NOTE: The first question requires a FORMULA, not a value. rad/sec = meters rad/sec

In the figure, a solid cylinder attached to a horizontal spring (k = 9.00 N/m) rolls without slipping along a horizontal surface. If the system is released from rest when the spring is stretched by 0.250 m, find (a) the translational kinetic energy and (b) the rotational kinetic energy of the cylinder as it passes through the equilibrium position. (c) If the cylinder has mass M = 5.30 kg, find the period of the simple harmonic motion that the cylinder's center of mass executes. (Hint: Find the time derivative of the total mechanical energy.) (a) Number i Units (b) Number i Units (c) Number i Units >

A simple pendulum comprised of a bob of mass  m = 172 g  and a lightweight string of length 76.0 cm is released from rest from an initial angle of 28.0° from the vertical. (a) Using the approach of simple harmonic motion, what is the maximum speed of the pendulum bob? m/s(b) Using the approach of simple harmonic motion, what is the maximum angular acceleration of the bob? rad/s2(c) How does the speed found in part (a) compare with that found by using a conservation of energy approach? (Assume that the values are nearly the same if within 10% of each other.) The speed is very different from that from part (a). The speed is nearly the same as that from part (a).

A 3kg block is attached to one end of a spring and resting on a frictionless surface. The mass is pulled away from rest and put to motion. A motion sensor is stationed to capture the data from the motion and we are given the following equation for the speed of the object in meters per second: v=-6.5 sin(4.0t). What would be the amplitude of the motion, the angular frequency, and the spring constant?