Dr. Nelson is at is again with Clem. She devises a toy for Clem to play with while she is at work teaching her students. The toy is a mouse-shaped block of mass m, oscillating on a spring with spring constant k. The block slides on a frictionless horizontal surface. m -A 0 +A The block has a mass of m= 100 g, and oscillates with a period of T = 0.50s. The spring is compressed so the block is released from rest at x = -10.0 cm. The block then oscillated back and forth between locations x = -10.0 cm and x = +10.0cm. a. Calculate k, the spring constant b. Write the equation for position as a function of time in the form x (t) = Acos(@t+ Po). Note you will need to find A, w, and do explicitly. c. At what x position does the block move with the greatest speed? Calculate the speed at this position. d. If the mass is doubled to 200 g, how long will it take the mass-spring system to complete one full oscillation?

Dr. Nelson is at is again with Clem. She devises a toy for Clem to play with while she is at work teaching her students. The toy is a mouse-shaped block of mass m, oscillating on a spring with spring constant k. The block slides on a frictionless horizontal surface. m -A 0 +A The block has a mass of m= 100 g, and oscillates with a period of T = 0.50s. The spring is compressed so the block is released from rest at x = -10.0 cm. The block then oscillated back and forth between locations x = -10.0 cm and x = +10.0cm. a. Calculate k, the spring constant b. Write the equation for position as a function of time in the form x (t) = Acos(@t+ Po). Note you will need to find A, w, and do explicitly. c. At what x position does the block move with the greatest speed? Calculate the speed at this position. d. If the mass is doubled to 200 g, how long will it take the mass-spring system to complete one full oscillation?

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Description: Dr. Nelson is at is again with Clem. She devises a toy for Clem to play with while she is at workteaching her students. The toy is a mouse-shaped block of mass m, oscillating on a spring withspring constant k. The block slides on a frictionless hori

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

Dr. Nelson is at is again with Clem. She devises a toy for Clem to play with while she is at work
teaching her students. The toy is a mouse-shaped block of mass m, oscillating on a spring with
spring constant k. The block slides on a frictionless horizontal surface.
m
-A
0
+A
The block has a mass of m= 100 g, and oscillates with a period of T = 0.50s.
The spring is compressed so the block is released from rest at x = -10.0 cm. The block then
oscillated back and forth between locations x = -10.0 cm and x = +10.0cm.
a. Calculate k, the spring constant
b. Write the equation for position as a function of time in the form x (t) = Acos(@t + p).
Note you will need to find A, w, and do explicitly.
c.
At what x position does the block move with the greatest speed? Calculate the speed at
this position.
d.
If the mass is doubled to 200 g, how long will it take the mass-spring system to complete
one full oscillation?

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