IB Physics SL C.1 Simple Harmonic Motion

[Maximum number: 6]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

Part 2 Vibrations and waves

The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).

(a)

Define simple harmonic motion (SHM).

[ 2 ]

(b)

D has mass $6.5 \times 10^{-3} \mathrm{~kg}$ and vibrates with amplitude 0.85 mm .

[ 4 ]

(i)

Calculate the maximum acceleration of D .

[ 2 ]

$\quad \omega=(2 \pi f=2 \pi \times 1250) 7854 \mathrm{rad} \mathrm{s}^{-1}$ ;

a_{0}=\left(-\omega^{2} x_{0}=-7854^{2} \times 0.85 \times 10^{-3}=\right)(-) 5.2 \times 10^{4} \mathrm{~ms}^{-2} ;

(ii)

Determine the total energy of D .

[ 2 ]

correct substitution into $E_{T}=\frac{1}{2} m \omega^{2} x_{0}{ }^{2}$ irrespective of powers of 10 ;

0.14 \text { to } 0.15 \mathrm{~J} ;

[Maximum number: 8]

This question is in two parts. Part 1 is about simple harmonic motion and forced oscillations. Part 2 is about electric and magnetic force fields.

Part 1 Simple harmonic motion and forced oscillations
The graph shows the variation with time of the displacement of an object undergoing simple harmonic motion.
displacement / mm

time / ms

(a)

State the amplitude of the oscillation.

[ 1 ]

(b)

Calculate the frequency of the oscillation.

[ 2 ]

period $=160 \mathrm{~ms}$ ;
frequency $=6.2 / 6.3 \mathrm{~Hz}$ ;

Marking guidance:

Allow ECF for incorrect period.

(c)

Determine the maximum speed of the object.

[ 2 ]

$\quad \omega=2 \pi \times 6.25$ ;
$v\left(=39.3 \times 32 \times 10^{-3}\right)=1.3\left(\mathrm{~m} \mathrm{~s}^{-1}\right) ;($ allow ECF from (a))
or
tangent drawn to graph at a point of zero displacement;
gradient calculated between 1.2 and 1.4;

(d)

The graph below shows how the displacement of the object varies with time. Sketch on the same axes a line indicating how the kinetic energy of the object varies with time. You should ignore the actual values of the kinetic energy.

[ 3 ]

[Maximum number: 8]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

(a)

Simple harmonic motion and waves

[ 8 ]

(i)

One end of a light spring is attached to a rigid horizontal support.

An object W of mass 0.15 kg is suspended from the other end of the spring. The extension x of the spring is proportional to the force F causing the extension. The force per unit extension of the spring k is $18 \mathrm{Nm}^{-1}$ .

A student pulls W down such that the extension of the spring increases by 0.040 m . The student releases W and as a result W performs simple harmonic motion (SHM).

[ 8 ]

(i)

State what is meant by the expression "W performs SHM".

[ 2 ]

(ii)

Determine the maximum acceleration of W .

[ 2 ]

$F=(18 \times 0.04=) 0.72 \mathrm{~N}$ ;

\text { acceleration }=\frac{0.72}{0.15}=4.8 \mathrm{~ms}^{-2} ;

(iii)

Determine the period of oscillation of the spring.

[ 3 ]

$\omega=\sqrt{\frac{a}{x}}$ ;
$=10.95 \mathrm{rads}^{-2}$ ;

T=\left(\frac{2 \pi}{\omega}=\right) \frac{6.28}{10.95}=0.57 \mathrm{~s} ;

(iv)

Determine the maximum kinetic energy of W .

[ 1 ]

$=1.4 \times 10^{-2}(\mathrm{~J})$ ;

[Maximum number: 2]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

Part 2 Vibrations and waves

The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).

Define simple harmonic motion (SHM).

[Maximum number: 2]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

Part 2 Vibrations and waves

The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).

D has mass $6.5 \times 10^{-3} \mathrm{~kg}$ and vibrates with amplitude 0.85 mm .

Calculate the maximum acceleration of D .

$\quad \omega=(2 \pi f=2 \pi \times 1250) 7854 \mathrm{rad} \mathrm{s}^{-1}$ ;

a_{0}=\left(-\omega^{2} x_{0}=-7854^{2} \times 0.85 \times 10^{-3}=\right)(-) 5.2 \times 10^{4} \mathrm{~ms}^{-2} ;

[Maximum number: 1]

This question is in two parts. Part 1 is about simple harmonic motion and forced oscillations. Part 2 is about electric and magnetic force fields.

Part 1 Simple harmonic motion and forced oscillations
The graph shows the variation with time of the displacement of an object undergoing simple harmonic motion.
displacement / mm

time / ms

State the amplitude of the oscillation.

[Maximum number: 3]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

Simple harmonic motion and waves

One end of a light spring is attached to a rigid horizontal support.

An object W of mass 0.15 kg is suspended from the other end of the spring. The extension x of the spring is proportional to the force F causing the extension. The force per unit extension of the spring k is $18 \mathrm{Nm}^{-1}$ .

A student pulls W down such that the extension of the spring increases by 0.040 m . The student releases W and as a result W performs simple harmonic motion (SHM).

Determine the period of oscillation of the spring.

$\omega=\sqrt{\frac{a}{x}}$ ;
$=10.95 \mathrm{rads}^{-2}$ ;

T=\left(\frac{2 \pi}{\omega}=\right) \frac{6.28}{10.95}=0.57 \mathrm{~s} ;

[Maximum number: 2]

This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a $100 \mathrm{k} \Omega$ fixed resistor R connected across a battery.

The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.

Part 2 Vibrations and waves

The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).

D has mass $6.5 \times 10^{-3} \mathrm{~kg}$ and vibrates with amplitude 0.85 mm .

Determine the total energy of D .

correct substitution into $E_{T}=\frac{1}{2} m \omega^{2} x_{0}{ }^{2}$ irrespective of powers of 10 ;

0.14 \text { to } 0.15 \mathrm{~J} ;

[Maximum number: 2]

This question is in two parts. Part 1 is about solar radiation and the greenhouse effect. Part 2 is about a mass on a spring.

Part 1 Solar radiation and the greenhouse effect
The following data are available.

(a)

The sketch graph below shows how the displacement of the object from point O varies with time over three time periods.

[ 2 ]

(i)

Label with the letter A a point at which the magnitude of the acceleration of the object is a maximum.

[ 1 ]

(ii)

Label with the letter V a point at which the speed of the object is a maximum.

[ 1 ]

[Maximum number: 1]

Object P moves vertically with simple harmonic motion (shm). Object Q moves in a vertical circle with a uniform speed. P and Q have the same time period T. When P is at the top of its motion, Q is at the bottom of its motion.

What is the interval between successive times when the acceleration of P is equal and opposite to the acceleration of Q?

A

$\frac{T}{4}$

B

$\frac{T}{2}$

C

$\frac{3 T}{4}$

D

T

IB Physics SL C 1 Simple Harmonic Motion Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question 3

Question (a)

Question (i)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question 4

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Question 6

Question 7

Question 8

Question 9

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Question (i)

Question (ii)

Question 10