Topic 13: Oscillations
1.3 Specification notice:
In order to develop their practical skills, students should be encouraged
to carry out a range of practical experiments related to this topic. Possible
experiments include measuring gravitational field strength using a simple
pendulum and measuring a spring constant from simple harmonic motion.
Mathematical skills that could be developed in this topic include
sketching relationships that are modelled by y = sin x, y = cos x.
13.Q Exam questions
13.181 understand that the condition for simple
harmonic motion is F = − kx, and hence understand
how to identify situations in which simple
harmonic motion will occur
what are the conditions for an object to ● An object’s acceleration or resultant
undergo SHM? force is proportional to displacement
from the equilibrium position
● Its acceleration or resultant force
must be directed towards the
equilibrium position
So…
A= -w2x from a prop -x
Thus, the same is expected of the restoring
forces
Why is SHM only a good approximation for a As the displacement (straight line path) is
pendulum at small angles? close enough to the curved path (until about
10 degrees)
, 13.182 be able to use the equations 𝑎 = −𝐴𝜔2 𝑥, 𝑥 =
𝐴𝑐𝑜𝑠 𝜔𝑡, 𝑣 = −𝐴𝜔𝑠𝑖𝑛 𝜔𝑡, 𝑎 = −𝐴𝜔2 𝑐𝑜𝑠 𝜔𝑡,
1 2𝜋
𝑎𝑛𝑑 𝑇 = = 𝑎𝑛𝑑 𝜔 = 2𝜋𝑓 as applied to a simple harmonic
𝑓 𝜔
oscillator
What are the equations for SHM for ● x = Acos(𝜔t)⍵
displacement, velocity and acceleration and ● v = -A𝜔sin(𝜔t)
how is acceleration related to displacement? ● a = -A𝜔2cos(𝜔t)
● a = -𝜔2x
What are the equations for SHM for ● xmax = A
displacement, velocity and acceleration at a ● vmax = -A𝜔
maximum value i.e a peak amplitude? ● amax = -𝜔2A
13.183 be able to use equations for a simple harmonic
𝑚 𝑙
oscillator 𝑇 = 2𝜋√ , and a simple pendulum 𝑇 = 2𝜋√
𝑘 𝑔
What are the equations for time period when
dealing with mass based oscillators and
𝑚
pendulums ● 𝑇 = 2𝜋√
𝑘
● T2 = 4𝜋2 x m/k
𝑙
● 𝑇 = 2𝜋√𝑔
● T2 = 4𝜋2 x l/g
1.3 Specification notice:
In order to develop their practical skills, students should be encouraged
to carry out a range of practical experiments related to this topic. Possible
experiments include measuring gravitational field strength using a simple
pendulum and measuring a spring constant from simple harmonic motion.
Mathematical skills that could be developed in this topic include
sketching relationships that are modelled by y = sin x, y = cos x.
13.Q Exam questions
13.181 understand that the condition for simple
harmonic motion is F = − kx, and hence understand
how to identify situations in which simple
harmonic motion will occur
what are the conditions for an object to ● An object’s acceleration or resultant
undergo SHM? force is proportional to displacement
from the equilibrium position
● Its acceleration or resultant force
must be directed towards the
equilibrium position
So…
A= -w2x from a prop -x
Thus, the same is expected of the restoring
forces
Why is SHM only a good approximation for a As the displacement (straight line path) is
pendulum at small angles? close enough to the curved path (until about
10 degrees)
, 13.182 be able to use the equations 𝑎 = −𝐴𝜔2 𝑥, 𝑥 =
𝐴𝑐𝑜𝑠 𝜔𝑡, 𝑣 = −𝐴𝜔𝑠𝑖𝑛 𝜔𝑡, 𝑎 = −𝐴𝜔2 𝑐𝑜𝑠 𝜔𝑡,
1 2𝜋
𝑎𝑛𝑑 𝑇 = = 𝑎𝑛𝑑 𝜔 = 2𝜋𝑓 as applied to a simple harmonic
𝑓 𝜔
oscillator
What are the equations for SHM for ● x = Acos(𝜔t)⍵
displacement, velocity and acceleration and ● v = -A𝜔sin(𝜔t)
how is acceleration related to displacement? ● a = -A𝜔2cos(𝜔t)
● a = -𝜔2x
What are the equations for SHM for ● xmax = A
displacement, velocity and acceleration at a ● vmax = -A𝜔
maximum value i.e a peak amplitude? ● amax = -𝜔2A
13.183 be able to use equations for a simple harmonic
𝑚 𝑙
oscillator 𝑇 = 2𝜋√ , and a simple pendulum 𝑇 = 2𝜋√
𝑘 𝑔
What are the equations for time period when
dealing with mass based oscillators and
𝑚
pendulums ● 𝑇 = 2𝜋√
𝑘
● T2 = 4𝜋2 x m/k
𝑙
● 𝑇 = 2𝜋√𝑔
● T2 = 4𝜋2 x l/g
