Q8. At higher altitude, g will decrease. According to the formula for the period of a simple pendulum, this will result in a greater period (or a smaller frequency). A pendulum clock counts the number of swings made by the pendulum and truly indicates not time, but the total number of swings of the pendulum. If the clock makes fewer swings in a time interval, the clock counts fewer total swings and indicates less time has elapsed and seems to "run slow."
Q9. The tire swing is essentially a simple pendulum. Push it to the side through a small angle and measure the period. Assume the standard value for "g" and use the formula for the period of a simple pendulum to calculate L.
Q13. A rattle in a car is a resonance phenomenon if it occurs only at or around a particular speed and not at other times. The frequency of the rotation of the unbalanced tire causing the problem equals the vibrational frequency of the rattling part.
The best way to do (b) is to make a sketch of x vs t and determine the times x = +A (spring compressed the most) and the times x = -A (spring stretched the most) from the sketch. Since you know the period, these times are simple multiples of the period (e.g. 1/4 T, 3/4 T, 5/4 T, 7/4 T, etc.). The times given above are exactly reversed. The times given for maximum extension are really those for maximum compression and vice versa.
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