# Physics simple harmonic oscillations

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#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
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
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(Original post by Fox Corner)
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0
4 years ago
#3
popped this in the physics forum for you
0
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
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:

----eqn(1)

where is the acceleration,
is the displacement and
is the angular frequency , given by .

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

----given by Joinedup

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

----eqn(2)

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

----eqn(3)

The maximum speed would occur when , so we have

----given by Joinedup
0
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
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