1. A mass is placed on a frictionless, horizontal table. A spring (k-105 N/m) which can be stretched or compressed, is placed on the table. A 3 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x= 2.6 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion in terms of the amplitude 'A', the angular velocity 'w', and the time 't'. Use the initial conditions to find the value of in the equations. Hint: Use the equation editor (orange button in the answer box) and find w in the greek letters. DO NOT USE numerical values for A and w for part (a). For example, a equation could be x(t) = Asin(wt). x(t) = v(t) = Position: x = m a(t) = (b) Calculate w for this spring-mass system. w = 5.77 rad/s Velocity: v = m/s (c) Find the position, velocity, and acceleration of the mass at time t=2 s. Use w up to 4 significant figures in the calculation. ✔m Acceleration: a = m/s² ES m m

1. A mass is placed on a frictionless, horizontal table. A spring (k-105 N/m) which can be stretched or compressed, is placed on the table. A 3 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x= 2.6 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion in terms of the amplitude 'A', the angular velocity 'w', and the time 't'. Use the initial conditions to find the value of in the equations. Hint: Use the equation editor (orange button in the answer box) and find w in the greek letters. DO NOT USE numerical values for A and w for part (a). For example, a equation could be x(t) = Asin(wt). x(t) = v(t) = Position: x = m a(t) = (b) Calculate w for this spring-mass system. w = 5.77 rad/s Velocity: v = m/s (c) Find the position, velocity, and acceleration of the mass at time t=2 s. Use w up to 4 significant figures in the calculation. ✔m Acceleration: a = m/s² ES m m

Name: 1. A mass is placed on a frictionless, horizontal table. A spring (k-
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Description: 1. A mass is placed on a frictionless, horizontal table. A spring (k-105 N/m) which can be stretched orcompressed, is placed on the table. A 3 kg mass is attached to one end of the spring, the other end isanchored to the wall. The equilibrium positi

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

1. A mass is placed on a frictionless, horizontal table. A spring (k-105 N/m) which can be stretched or
compressed, is placed on the table. A 3 kg mass is attached to one end of the spring, the other end is
anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=
2.6 cm and releases it from rest. The mass oscillates in SHM.
(a) Determine the equations of motion in terms of the amplitude 'A', the angular velocity 'w', and the
time 't'. Use the initial conditions to find the value of in the equations.
Hint: Use the equation editor (orange button in the answer box) and find w in the greek letters. DO
NOT USE numerical values for A and w for part (a).
For example, a equation could be x(t) = Asin(wt).
x(t) =
v(t) =
a(t) =
w = 5.77
(b) Calculate w for this spring-mass system.
rad/s
Position: x =
m
Velocity: v =
m/s
(c) Find the position, velocity, and acceleration of the mass at time t=2 s. Use w up to 4 significant
figures in the calculation.
Acceleration: a =
m/s²
✔m
S

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