1. (a) What is the expression for the mechanical energy of the Equilibrium Position spring-mass system at any instant of time (Chapter # 9 slides). In the shown system the spring's constant is 2.50 N/cm m and the mass is 180 g. If you stretch the spring a distance A = 12 cm and then release it. (b) What is the energy of the system? (c) What is the maximum speed of the mass? (Hint maximum speed is attained when displacement from equilibrium position is zero) 2. In the figure, the left end of the tube is closed while the right end is open. The tuning fork oscillates at 480 Hz and produces the shown standing sound wave. (a) What is the length of the tube? (b) What is the frequency of the next harmonic (you must draw a sketch) (Take the velocity of sound 343 m/s) (You have to figure out how to No displacement approach this problem, it was explained on the lecture of Tue 1 1/28/2023) Maximum displacement 3. The conducting surface of a Van de Graaff generator is approximated to a sphere with diameter 15 cm. (a) If it is charged until the voltage of the sphere relative to the ground becomes 300 k V, how much charge has been transmitted as corona to the hand of a person (as shown). (b) what is the power of the resulting corona if it lasts 0.1 s? (Apply V = kQ/R, k = 9x 10' Nm?/C2, then Ue = QV, then expression of power) 4. (a) In the diagram, the peak-peak voltage is 340 V, what is the root mean square value, Vims? (b) If this voltage is feeding a heating coil for a dryer having a power of 1.5 kW, what is the resistance of the coil? (c) How much charge pass through the drier circuit in one minute? (All parts were explained during the lecture of 1 1/30/2023)