Answer Happy

please solve these questions
4. A block-spring oscillator exhibits simple harmonic motion with an amplitude A and its maximum speed is Umax. [1] [1] (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 (v). 1 (c) When the block's speed is - Umar, show that the distance (lm) from the central equilib- 2 rium position is: 3mw2 AP V 42 I'm = 1 2 (d) When the block’s position is į A, show its speed (v) is given by: - U = 1 W2 A2 KA? 4m 5. A satellite of mass 2000 kg is in a circular orbit about the Earth. It is at a height of 1.4 x 107 m above the Earth's surface. The Earth's radius and mass are 6378 km and 5.97 x 1024 kg, respectively. (a) Calculate the magnitude of the gravitational force of the Earth on the satellite. (b) How fast is the satellite travelling? (c) Determine how many orbits the satellite makes around the Earth per day. [2] [3] [5]