NYJC_EJC 2026 Oscillations and Waves Tutorial

9814 H3 Physics (2026) Oscillations and Wave Motion Tutorial 1 Oscillations 1 (a) What are the conditions for simple harmonic motion? [2] (b) A point mass moves along the line AB (Fig. 1.1) with simple harmonic motion of amplitude 0.040 m and period 1.6 s. Fig. 1.1 At time t = 0, the mass is at the equilibrium position O, and is moving in the direction OA. What is the displacement of the mass at time t = 1.3 s? In which direction is it moving at this instant? [6] (c) An ideal spring of unstretched length L and force constant k is fastened between two fixed points X and Y a distance L apart just above a horizontal, frictionless table. A mass M is then clamped to the mid -point of the spring so that it rests on the table. The mass is drawn aside through a small distance x, perpendicular to the original line of the spring, and is then released, as shown in plan view in Fig. 1.2. Fig. 1.2 Find the initial acceleration of the mass, and hence determine whether the resulting oscillations are simple harmonic. (Hint: for ( )1, 1 1 n z z nz + = + ) [8] (d) Why is simple harmonic motion so important in Physics? [4] [N93/P1/Q4] 2 (a) A straight wire has unstretched length L and area of cross-section A. Find the relation between the force constant k of the wire and the Young modulus E of the metal of which it is made. Why does this relation not apply to a spring in the form of a coil of the same wire? [4] x

9814 H3 Physics (2026) Oscillations and Wave Motion Tutorial 2 (b) A mass m is supported by a spring of force constant k. A simple derivation shows that the period T of vertical oscillations of the mass is given by ( ) 12 2T m k= . What assumptions must be made if this expression is to hold? (You are not asked to derive the expression.) [3] (c) A mass M is supported by two springs, of force constants k1 and k2 respectively, connected in series as shown in Fig. 2.1. Fig. 2.1 Find the effective force constant of the spring combination, and hence deduce the period of vertical oscillation of the mass. [4] (d) The mass M is now set between the same two springs on a horizontal, frictionless surface, as shown in Fig. 2.2. Each spring is of unstretched length l. The distance between the clamps at each side is D, where D is greater than 2l. Fig. 2.2 (i) Find the distance d of the equilibrium position of the mass from the left - hand clamp. [3] (ii) The mass is then displaced a distance x to the right of the equilibrium position, along the axis of the springs. The distance x is sufficiently short for both springs to remain in tension. Show that, when released, the mass moves with simple harmonic motion. Find the period of the oscillations. [6] [N95/P1/Q7]

9814 H3 Physics (2026) Oscillations and Wa