Texts: [QUESTION 2] [14 MARKS]
Hooke's law is mathematically expressed as:
F(x) = -kx
A mass attached to the end of a spring obeys Hooke's law and executes oscillations of the type that we call simple harmonic motion.
2.1. Distinguish between simple harmonic motion, damped oscillations, and forced oscillations. [3]
2.2. From the mathematical representation of Hooke's law, what does k, x, and the (-) sign represent? [3]
2.3. By analyzing Hooke's expression, what can you say about the force
2.3.1 when x = 0? [2]
2.3.2 When x > 0? [2]
2.3.3 When x < 0? [2]
2.4. From your analysis above, what can you conclude about Hooke's law and under which circumstances is the law valid? [2]
QUESTION 3 [18 Marks]
3.1. By definition, what is meant by central force? [2]
3.2. What is the equivalent definition in terms of potential energy of the system? [2]
3.3. Give the mathematical relation that links the force in view of the two definitions. [2]
3.4. Give three examples of central forces. [3]
3.5.
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3.6. Angular momentum plays a key role in dealing with central forces because it is constant over time. Suppose the angular momentum, L, of a point mass is given by:
L = 7xp
By the nature of the cross product, what two properties does L have? [2]
3.7. Show that: If a particle is subject to a central force only, then its angular momentum is conserved, i.e., if V(r) = V(r), then dL/dt = 0. [5]
