A mass m - 2.07 kg is attached to a spring of force constant k - 46.9 N/m and set into oscillation on a horizontal frictionless surface by stretching it an amount A - 0.19 m from its equilibrium position and then releasing it. The figure below shows the oscillating mass and the particle on the associated reference circle at some time after its release. The reference circle has a radius A, and the particle traveling on the reference circle has a constant counterclockwise angular speed w, constant tangential speed V- cA, and centripetal acceleration of constant magnitude a.- wA. (a) Determine the following. maximum speed of the oscillating mass m/s magnitude of the maximum acceleration of the oscillating mass +A m/s2 magnitude of the maximum force experienced by the oscillating mass N maximum kinetic energy of the oscillating mass maximum elastic potential energy the spring attached to the mass total energy of the oscillating mass-spring system (c) If the record of time starts when x- 0 and v= taA, determine expressions for the displacement, velocity, and acceleration of the oscillating mass along the x-axis at any time t later. (Your expression should be in terms of the variable t and other numerical values. Assume any numerical values in your expression are in standard SI units, but do not enter units into your expression. ) (b) If the record of time starts when x- +A and v- 0, determine expressions for the displacement, velocity, and acceleration of the oscillating mass along the x-axis at any time t later. (Your expression should be in terms of the variable t and other numerical values. Assume any numerical values in your expression are in standard SI units, but do not enter units into your expression.)
A mass m - 2.07 kg is attached to a spring of force constant k - 46.9 N/m and set into oscillation on a horizontal frictionless surface by stretching it an amount A - 0.19 m from its equilibrium position and then releasing it. The figure below shows the oscillating mass and the particle on the associated reference circle at some time after its release. The reference circle has a radius A, and the particle traveling on the reference circle has a constant counterclockwise angular speed w, constant tangential speed V- cA, and centripetal acceleration of constant magnitude a.- wA. (a) Determine the following. maximum speed of the oscillating mass m/s magnitude of the maximum acceleration of the oscillating mass +A m/s2 magnitude of the maximum force experienced by the oscillating mass N maximum kinetic energy of the oscillating mass maximum elastic potential energy the spring attached to the mass total energy of the oscillating mass-spring system (c) If the record of time starts when x- 0 and v= taA, determine expressions for the displacement, velocity, and acceleration of the oscillating mass along the x-axis at any time t later. (Your expression should be in terms of the variable t and other numerical values. Assume any numerical values in your expression are in standard SI units, but do not enter units into your expression. ) (b) If the record of time starts when x- +A and v- 0, determine expressions for the displacement, velocity, and acceleration of the oscillating mass along the x-axis at any time t later. (Your expression should be in terms of the variable t and other numerical values. Assume any numerical values in your expression are in standard SI units, but do not enter units into your expression.)
College Physics
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Chapter1: Units, Trigonometry. And Vectors
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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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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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Transcribed Image Text:A mass m = 2.07 kg is attached to a spring of force constant k = 46.9 N/m and set into oscillation on a horizontal frictionless surface
by stretching it an amount A = 0.19 m from its equilibrium position and then releasing it. The figure below shows the oscillating mass
and the particle on the associated reference circle at some time after its release. The reference circle has a radius A, and the particle
traveling on the reference circle has a constant counterclockwise angular speed w, constant tangential speed V = wA, and centripetal
acceleration of constant magnitude a.
w²A.
(a) Determine the following.
maximum speed of the oscillating mass
m/s
magnitude of the maximum acceleration of the oscillating mass
+A
m/s2
x =-A
V = @A
magnitude of the maximum force experienced by the oscillating mass
N
a̟= w³A
ot
maximum kinetic energy of the oscillating mass
maximum elastic potential energy of the spring attached to the mass
total energy of the oscillating mass-spring system
(c) If the record of time starts when x = 0 and v = +wA, determine expressions for the displacement, velocity, and acceleration
of the oscillating mass along the x-axis at any time t later. (Your expression should be in terms of the variable t and other
numerical values. Assume any numerical values in your expression are in standard SI units, but do not enter units into your
expression.)
(b) If the record of time starts when x = +A and v = 0, determine expressions for the displacement, velocity, and acceleration
X =
of the oscillating mass along the x-axis at any time t later. (Your expression should be in terms of the variable t and other
numerical values. Assume any numerical values in your expression are in standard SI units, but do not enter units into your
v =
expression.)
X =
a =
V =
a =
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