Physics simple harmonic oscillations

Watch
amy1999
Badges: 3
Rep:
?
#1
Report Thread starter 4 years ago
#1
Part of a building structure is oscillating with approximately simple harmonic motion with a period of 10 s and amplitude 1 m.
a) calculate the maximum speed of the oscillation.
b) calculate the maximum acceleration of the oscillation.
Can you explain how to work these out please as I have no clue, the equations are confusing me.
0
reply
TSR Jessica
Badges: 19
Rep:
?
#2
Report 4 years ago
#2
Sorry you've not had any responses about this. Are you sure you've posted in the right place? Here's a link to our subject forum which should help get you more responses if you post there.


Just quoting in Fox Corner so she can move the thread if needed :wizard:
Spoiler:
Show
(Original post by Fox Corner)
x
0
reply
Fox Corner
Badges: 21
Rep:
?
#3
Report 4 years ago
#3
:wizard: popped this in the physics forum for you
0
reply
Joinedup
Badges: 20
Rep:
?
#4
Report 4 years ago
#4
The relevant equations appear in the formula book as

vmax=2πfA
amax=(2πf)2 A

A (capital) is the amplitude
f is the frequency of oscillation... which is 1/T (T is the period in seconds)
1
reply
Eimmanuel
Badges: 13
Rep:
?
#5
Report 4 years ago
#5
(Original post by amy1999)
Part of a building structure is oscillating with approximately simple harmonic motion with a period of 10 s and amplitude 1 m.
a) calculate the maximum speed of the oscillation.
b) calculate the maximum acceleration of the oscillation.
Can you explain how to work these out please as I have no clue, the equations are confusing me.
In simple harmonic motion, the acceleration is always directly proportional to displacement and has the following defining equation:

 a = - \omega^2 x ----eqn(1)

where  a is the acceleration,
 x is the displacement and
 \omega is the angular frequency , given by  \omega = 2 \pi f = \frac{2 \pi}{T} .

From eqn(1), the maximum value of acceleration occurs at when the displacement is maximum - maximum displacement implies amplitude, A.

So the maximum acceleration is

 a = \omega^2 A = (2 \pi f)^2 A ----given by Joinedup

The displacement of simple harmonic motion can be described by a sinusoidal function

 x = A \cos( \omega t) ----eqn(2)

If equation (2) is differentiated with respect to time t, we obtain the "velocity"

 v = -\omega A\sin( \omega t) ----eqn(3)

The maximum speed would occur when  \sin( \omega t) = \pm 1 , so we have

 v = \omega A = (2 \pi f)A ----given by Joinedup
0
reply
swinroy
Badges: 12
Rep:
?
#6
Report 1 year ago
#6
(Original post by amy1999)
Part of a building structure is oscillating with approximately simple harmonic motion with a period of 10 s and amplitude 1 m.
a) calculate the maximum speed of the oscillation.
b) calculate the maximum acceleration of the oscillation.
Can you explain how to work these out please as I have no clue, the equations are confusing me.
The max speed is the angular speed x Amplitude
The angular speed is calculated as follows: 2 x Pi divided by Period

THe max acceleration is the previous answer x angular speed

if you liken circular motion to SHM
one revolution is equivalent to one complete oscillation
in both cases 2 Pi RADIANS are performed in a periodic time
The angular speed is the number or RADIANS performed per SECOND
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Should 'Mental health support' be included on league tables?

Yes (188)
74.6%
No (64)
25.4%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise