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Assignment

This assignment is OPTIONAL can addUP TO 1.5 to your overall 4A grade equivalentto one la

The goal of this assignment is to better understandthe last question on theHooke's Law La

You may have observed that the oscillationwas symmetric about the mass equili

iumrather than the natural length You willshow graphically that when the object isat the mass equili

ium the potential energy ofsystem is minimized it is a stable equili

ium

We know that the force on the object thepotential energy of the system are related by

É JU

which reduces to

Fy day

for one dimensional motion

My

Natural

length

Turning

Mass Xy

points

equili

ium On

1 Define the system to be mass springEarth Plot the gravitational potential

energy the spring potential energyUgly Usp y on the same set of axesU on the vertical axis y on horizontal

It is not necessary to scale the axessimply sketch the shapes of the plots

Let the x axis pass through the natural

length SO Ug o there

all

y o co

esponds

Fy

w hat length

sample axes

2 Find the total potential energy function Uly

y adding Ugly Usp y Plot u lyon another set of axes

Do this by hand no calculator Desmosshow work

Hint complete the square

3 U ly is parabolic Determine the coordinatesof the vertex label it on the

parabola Express the coordinates in terms of

M K g constant s

Do you recognize the y coordinate of thevertex This is a special vertical position

what is it

4 Label the regions on the plot where thenet force is directed up where the

net force is directed down

Hint Fy day

5 Add a horizontal line representing thetotal energy of the system to the plotThe line should be above the horizontal

axis

Label the turning points on the plot

Are the turning points symmetric aboutthe natural length or the massequili

ium

6 Does the choice of coordinate system mattershow that the y coordinate of Umin isindependent of coordinate system

For example you could let y o co

espondw mass equili

ium rather than

natural length repeat steps 1 3 above

Answered 1 days AfterFeb 07, 2022

Solution

1. Consider a simple 1-D mass spring system consisting of a massive block hung from one end

of a perfectly elastic massless spring and other end is fixed at a point.

Let h=0 be the point where gravitational potential energy Ug is zero and equili

ium position

e the point where spring potential energy Usp is zero.

As suggested in the question, we have taken x-axis to be passing through the natural length

so Ug=0

m

m

y

y

Highest point (H.P.)

Equili

ium point (E.P.)...

1. Consider a simple 1-D mass spring system consisting of a massive block hung from one end

of a perfectly elastic massless spring and other end is fixed at a point.

Let h=0 be the point where gravitational potential energy Ug is zero and equili

ium position

e the point where spring potential energy Usp is zero.

As suggested in the question, we have taken x-axis to be passing through the natural length

so Ug=0

m

m

y

y

Highest point (H.P.)

Equili

ium point (E.P.)...

SOLUTION.PDF## Answer To This Question Is Available To Download

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