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4. A block-spring oscillator exhibits simple harmonic motion with an amplitude A and its maximum speed is Vmax [ (a) Write a mathematical expression for the total energy of an oscillator in terms of its angular frequency, w, mass (m), and its amplitude A. (b) Write a mathematical expression for the total energy of an oscillator in terms of its position (x), mass (m), spring constant (k) and speed (u). (c) When the block's speed is Umaz, show that the distance (mm) from the central equilib- 2 rium position is: 3mw2 A2 4k 1 xm 1 (d) When the block's position is į A, show its speed (v) is given by: V= Iw2 A2 KA2 4m