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An object attached to a spring vibrates with
(a) For this motion, find the amplitude.
(b) For this motion, find the period.
(c) For this motion, find the angular frequency.
(d) For this motion, find the maximum speed.
(e) For this motion, find the maximum acceleration.
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- A 2.38 kg ball is attached to an unknown spring and allowed to oscillate. The figure shows a graph of the ball's position x as a function of time t. For this motion, what is the period? What is the frequency? What is the angular frequency?A spring is attached to the ceiling and pulled 12 cm down from equilibrium and released. The amplitude decreases by 10% each second. The spring oscillates 18 times each second. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t.A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 3.40 cm, and the frequency is 2.10 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.) X = (b) Determine the maximum speed of the particle. cm/s (c) Determine the earliest time (t > 0) at which the particle has this speed S (d) Find the maximum positive acceleration of the particle. cm/s² (e) Find the earliest time (t > 0) at which the particle has this acceleration. (f) Determine the total distance traveled between t = 0 and t = 0.71 s. cm
- A 2.36 kg ball is attached to an unknown spring and allowed to oscillate. The figure (Figure 1) shows a graph of the ball's position as a function of time t. Figure x (cm) 3.0 2.0 1.0 -1.0 -2.0 -3.0 1 of 1 A 1.0 0.50 t(s) What is the amplitude? Express your answer in centimeters to one decialm place. A = Submit Part E VE ΑΣΦ k= Answer ? What is the force constant of the spring? Express your answer in newtons per meter to three significant figures. ΨΕ ΑΣΦ cm ? N/mIn simple harmonic motion, when is the speed the greatest? (There could be more than one correct choice.) Check all that apply. 1. When the potential energy is a zero 2. When the magnitude of the acceleration is a maximum 3. When the displacement is a maximum 4. When the potential energy is a maximum 5. When the magnitude of the acceleration is a minimumAn object executes simple harmonic motion with an amplitude A. (Use any variable or symbol stated above as necessary.) (a) At what values of its position does its speed equal half its maximum speed? x = ± (b) At what values of its position does its potential energy equal half the total energy? x = ±
- Does the period of oscillation depend on the hanging mass? Justify your answer.Does the period of oscillation vary with the amplitude of oscillation, if you keep the hanging mass constant? Justify your answer.A block of mass m = 1 kg is attached a spring of force constant k = 500 N/m as shown in the figure below.The block is pulled to a position x = 10 cm to the right of equilibrium and released from rest. The horizontalsurface is frictionless.(a) What’s the period of block’s oscillation? (b) Find the speed of the block as it passes through the equilibrium point x = 0. (c) Please represent block’s motion with the displacement vs. time function x(t) and draw the motiongraph x(t) for at least one periodic cycle. Note, please mark the amplitude and period in the motiongraph. Assume the clock starts from when the block is just released. (d) Please find out the block’s velocity and acceleration at t = 0.14s.A particle moves in simple harmonic motion with a period of 0.3 s and an amplitude of 6 cm. What are the speed and acceleration of the particle when it is 4 cm from the equilibrium position?