1.SHMC

Question 1

U13PH4 ) The car travels over a series of speed humps. This results in a driving force of frequency 1.24Hz. Explain what happens to the oscillation of the platform in the suspension system.

Answer 1

1）f=f_d=1.25Hz

2）f_d=f₀

3)A↑

Question 2

U13PH4 Explain the purpose of damping in a car suspension system. [3]

Answer 2

1. quickly to eql
2. critical damping
3. resonance

Question 3

U13PH4 State what is meant by Simple Harmonic Motion (SHM). [2]

Answer 3

A body moves with SHM if its acceleration

• is directly proportional to its displacement from a fixed point
• is always directed towards that [fixed] point

Question 4

U12PH4 (iv) Give a practical example of resonance. Identify the driving force of the system and the responding oscillator. [3]

Answer 4

microwave cooking (1)

driving force : by microwave radiation (1)

responding oscillator : water molecules (1)

Question 5

U12PH4 Define simple harmonic motion.

Answer 5

Acceleration ∝ displacement from central (fixed) point (1) is directed towards the central (fixed) point (1)

Question 6

U12PH4 Suggest a cause for the observed damping. [1]

Answer 6

air resistance

magnetic damping

friction by itself is not enough - needs either reference or

Question 7

U12PH4 (iii) Explain what is meant by resonance. [1]

Answer 7

At a certain driving frequency there is a maximum (peak) in the amplitude of the oscillating load. At this frequency the system is at resonance.

Question 8

U12PH4

Answer 8

Question 9

U12PH4 (c) Explain what is meant by centripetal acceleration. [1]

Answer 9

A body moving in a circular motion experiences an acceleration towards the centre of the circle. This is known as centripetal acceleration.

Question 10

(c) When people walk across this bridge, oscillations of large amplitude occur. Explain the cause of the large-amplitude oscillations and the possible consequences. [3]

Answer 10

natural frequency (period) close to walking frequency (period) (1)

resonance occurs (1)

which could break (or damage) bridge (1)

Question 11

(iii) Suggest a way in which the experiment can be improved. [1]

Answer 11

Take measurements for each value of R several times

measure time of more rotations

use of video capture

increase radius and period

Accept repeat readings

Question 12

(ii) By considering these forces show that: resultant force component on the mass along the arc = – mg sinθ You may add to the diagram if you wish. [3]

Answer 12

T does not have a component tangential to the arc (1)

Component of mg tangential to the arc is 𝑚𝑔 sin𝜃, (1) this is in the opposite direction to s (or 𝜃) and so the negative sign (1)

Question 13

Discuss whether the equation in part (a)(iii) satisfies the definition of simple harmonic motion. [2]

Answer 13

Acceleration ∝ 𝜃 (or 𝑠) measured [from a fixed position] (1) and opposite in direction (-ve) so SHM (1)

Question 14

) If the maximum displacement angle of the mass is 0.067rad, justify the use of simple harmonic motion in part (b)(i). [2]

Answer 14

For maximum distance along the arc 𝜃max = 0.067, also sin 𝜃max = 0.067 As 𝜃max = sin 𝜃max (i.e. for the largest value of 𝜃) (1)

then sin 𝜃 = 𝜃 for all 𝜃, and approximation holds for SHM. System oscillates with SHM (1)