4. Simple Harmonic Motion: An object is attached to a coiled spring. It is pulled down a distance of 6 inches from its equilibrium position and released. The period of the motion is 4 seconds. a. Show your work for modeling an equation of the objects simple harmonic motion d = a cos wt where d is distance from the rest position and the period is, > 0. A hand sketch may be helpful, but is not required. b. What is the frequency? c. When t = 3 find the distance and interpret it.
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- A horizontal spring has a force constant 7.98 N/m and is attached to a wall at one end. A block of wood of mass 366 g is attached to the the other end. We assume that this system sits on a frictionless surface. The block is displaced by +6.90 cm from equilibrium and released from rest. a. What is the period of the motion? S b. What is the equation that describes the position of the block? Make sure to show your work in your notes. -6.90 x102 m cos (4.67 t) O 6.90 ×102 m cos (4.67 t) 6.90 x102 m cos (7.98 t+ 7/2) O 6.90 ×102 m cos (7.98 t) -6.90 x102 m cos (7.98 t) O 6.90 x102 m cos (4.67 t + T/2) c. What is the equation that describes the speed of the block? Make sure to show your work in your notes. -0.322 m/s sin (4.67 t) -0.551 m/s cos (7.98 t) -0.322 m/s sin (4.67 t + T/2) -0.551 m/s sin (7.98 t+ T/2) -0.322 m/s cos (4.67 t) -0.551 m/s sin (7.98 t)On the axes, draw a graph of the period of a pendulum as a function of its length. a. Explain the shape of the graph you have drawn. Is it linear or curved, and why? b. If you wanted to double the period of a pendulum, what change would you make to its length?A mass hanging from a spring undergoes vertical simple harmonic motion.a. Where in the motion is the magnitude of the net force equal to zero?b. Where in the motion is the velocity equal to zero?c. Where in the motion does the acceleration have its greatest magnitude?d. Where in the motion is the spring force equal to zero?
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- Pendulum Problems 1. A pendulum has a frequency of 2.0 Hz. What is the period of the pendulum? What is the length of the pendulum? 2. The period of the "second hand" on a clock is 60.0 seconds (duh). What is the frequency of the "second hand" in Hz? What length pendulum would have the same period? 3. A pendulum at a science museum is set up so that it has a length of 2.75 m. What is its period? How long would a second pendulum have to be in order to have a period that is half as much?T 56. Damped sine wave The graph of f(t) = e¯' sin t is an example of a damped sine wave; it is used in a variety of applications, such as modeling the vibrations of a shock absorber. a. Use a graphing utility to graph ƒ and explain why this curve is called a damped sine wave. b. Compute f'(1) and use it to determine where the graph of f has a horizontal tangent. c. Evaluate lim e¯ª sin t by using the Squeeze Theorem. What does the result say about the oscillations of this damped sine wave?An object moves in simple harmonic motion described by the equation d=4 cos t, where t is measured in seconds and d in inches. Find the following. a. the maximum displacement b. the frequency c. the time required for one cycle a. in. b. cycles per second C. Enter your answer in the answer bos Save for Later Type here to search
- 10. A block hangs on a spring attached to the ceiling and is pulled down 6 inches below itsequilibrium position. After release, the block makes one complete up-and-down cycle in 2seconds and follows simple harmonic motion. a. What is the period of the motion? b. What is the frequency? c. What is the amplitude? d. Write a function to model the displacement ? (in inches) as a function of the time ? (in seconds) after release. Assume that a displacement above the equilibrium point is positive.e. Find the displacement of the block and direction of movement at ? = 1 sec.These three questions are based on the information in #1. PLEASE ANSWER THEM. They're all connected. Thank you!!Find amplitude, period, frequency and/or angular frequency. The numbers I put are my guesses, but idk if they're right