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Optics

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Submitted By Roshea
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Unit One
Worksheet 1
1. A particle undergoes SHM with amplitude of 4.0mm and angular frequency of 2.0 s-1. At t = 0, the displacement is 2 2 mm. Write down the equation of displacement for this motion. 2. A particle undergoes SHM with amplitude of 8.00 cm and an angular frequency of 0.25 s-1.
At t = 0 the velocity is 1.24 cm s-1.
(a) Write down the equation for displacement and velocity for this motion.
(b) Calculate the initial displacement.
(c) Calculate the first time at which the particle is at x = 2.00 cm and x = - 2.00 cm.
3. (a) Calculate the length of a pendulum that has a period equal to 1.00s.
(b) Calculate the percentage increase in the period of a pendulum when the length is increased by 4.00%.
4. The graph in the figure shows the variation with displacement x of the acceleration ‘a’ of the particle.

(a) Explain how it may be deduced that the particle executes SHM.
(b) Use the graph to determine the period of oscillations

(c) The maximum speed of the body during oscillations.
5. The graph in the figure shows the displacement of a particle from a fixed equilibrium position. (a) Use the graph to determine: (i) the period of motion (ii) the maximum velocity of the particle during oscillation, and (iii) the maximum acceleration experienced by the particle.
(b) On a copy of the diagram, mark (i) a point where the velocity is zero ( label this as Z)
(ii) a point where the velocity is positive and has the largest magnitude ( label this as V)
(iii) a point where the acceleration is positive and has the largest magnitude ( label this as
A).
6. A body of mass m is placed on a horizontal plate that under goes vertical SHM The amplitude of SHM is A and the frequency is f.

(a) Derive an expression for the reaction force on the particle from the plate when the particle is at its highest position.

(b) Using the expression in

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