Discuss the below:
Q1. A 2 kg block is attached to a spring and placed on a horizontal smooth surface. A horizontal force of 20 N is required to hold the block at rest when it is pulled 0.2 m from its equilibrium position. The block is released from its rest from this point, and is subsequently undergoes simple harmonic motion. Find a) the spring stiffness; b) the frequency of oscillations; c) the maximum speed of the block. Where does this maximum speed occur? Find the total energy of the oscillating system. Find the speed when the position equals one third of the maximum value.
Q2. How does the natural frequency of swing change when you move from sitting down to standing up?
Q3. You stand just to the side of the low point of a child's swing and always push the child in the same direction. Which of the following multiples of the fundamental frequency will not produce resonance: ¹/3, ½, 1, or 2?
Q4. A string fixed at both ends and having a mass of 4.8 g, a length of 2 m, and a tension of 48 N vibrates in its second normal mode. What is the wavelength in the air of the sound emitted by this vibrating string?
Q5. In the following list of properties of periodic waves, which one is independent of the others: frequency, wavelength, speed, amplitude? What happens to the wavelength if both the speed of the wave and the frequency are cut in half?
Q6. A longitudinal standing wave can be established in a long aluminum rod by stroking it with rosin on your fingers. If the rod is held tightly at its midpoint, what is the fundamental standing wave? Assume that there are antinodes at each end of the rod and node where the rod is held.
Q7. Draw a diagram to present the standing wave pattern for the fourth harmonic of a rope fixed at both ends.