A 270-g block connected to a light spring for which theforce constant is 6.30 N/m is free to oscillate on ax= 0frictionless, horizontal surface. The block is displacedt= 05.20 cm from equilibrium and released from rest as inthe figure.X; = AU; = 0(A) Find the period of its motion.A block-spring system that begins itsmotion from rest with the block at x = A at t(B) Determine the maximum speed of the block.= 0. In this case, o = 0; therefore, x = A cosot.(C) What is the maximum acceleration of the block?(D) Express the position, velocity, and acceleration as functions of time in SI units.SOLVE IT(A) Find the period of its motion.Conceptualize Study the figure and imagine the block moving back and forth in simple harmonic motiononce it is released. Set up an experimental model in the vertical direction by hanging a heavy object suchas 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 theangular frequency of the block-spring6.30 N/m270 x 10-3 kgmsystem:= 4.83 rad/sUse the equation to find the period of the27T%3D2nsystem:4.83 rad/s(B) Determine the maximum speed of the block.Use the equation to find vmay:Vmax = wA = (4.83 rad/s)(5.20 x 10-2 m)m/sMacBook Proesc**:::@2#32$%&234578.QWTY UD< CO%24

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Description: A 270-g block connected to a light spring for which theforce constant is 6.30 N/m is free to oscillate on ax= 0frictionless, horizontal surface. The block is displacedt= 05.20 cm from equilibrium and released from rest as inthe figure.X; = AU; = 0(A

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A 270-g block connected to a light spring for which the x=0 A force constant is 6.30 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced t= 0 5.20 cm from equilibrium and released from rest as in the figure. (A) Find the period of its motion. A block-spring system that begins its motion from rest with the block at x = A at t (B) Determine the maximum speed of the block. = 0. In this case, o = 0; therefore, x = A cos ot. (C) What is the maximum acceleration of the block? (D) Express the position, velocity, and acceleration as functions of time in SI units.

A 270-g block connected to a light spring for which the x=0 A force constant is 6.30 N/m is free to oscillate on a frictionless, horizontal surface. The block is displaced t= 0 5.20 cm from equilibrium and released from rest as in the figure. (A) Find the period of its motion. A block-spring system that begins its motion from rest with the block at x = A at t (B) Determine the maximum speed of the block. = 0. In this case, o = 0; therefore, x = A cos ot. (C) What is the maximum acceleration of the block? (D) Express the position, velocity, and acceleration as functions of time in SI units.

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.

Topic Video

Question

A 270-g block connected to a light spring for which the
force constant is 6.30 N/m is free to oscillate on a
x= 0
frictionless, horizontal surface. The block is displaced
t= 0
5.20 cm from equilibrium and released from rest as in
the figure.
X; = A
U; = 0
(A) Find the period of its motion.
A block-spring system that begins its
motion from rest with the block at x = A at t
(B) Determine the maximum speed of the block.
= 0. In this case, o = 0; therefore, x = A cos
ot.
(C) What is the maximum acceleration of the block?
(D) Express the position, velocity, and acceleration as functions of time in SI units.
SOLVE IT
(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
6.30 N/m
270 x 10-3 kg
m
system:
= 4.83 rad/s
Use the equation to find the period of the
27
T%3D
2n
system:
4.83 rad/s
(B) Determine the maximum speed of the block.
Use the equation to find vmay:
Vmax = wA = (4.83 rad/s)(5.20 x 10-2 m)
m/s
MacBook Pro
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