1) Given the equation x = 0.5 cos (0.75 π t), what is the amplitude of the wave?
2)Given the equation x = 0.5 cos (0.68 π t), what is the angular frequency of the wave? (Give the numeric value to 3 sig. fig.)
3) Given the equation of motion for a spring mass system x = 0.8 cos (0.33 π t), what is the spring constant if the mass attached to the spring is 0.25 Kg?
4) Given a spring and mass system, where the spring constant is 10 N/m and the mass is 0.25 Kg, what would the angular frequency of the system if it were placed into motion?
5) Neil Armstrong is on the moon (gravity of the moon is one sixth that of earth). If he is using a 1 meter pendulum, what would the observed period of one cycle of the pendulum be?
6) A clock is set to keep time using a pendulum. After watching the clock over a period of 24 hours, it was determined that the time was off by a five minutes, i.e. the clock indicated that the day was 24.083 hours rather than the 24.000 hours it should have been. Should the pendulum be lengthened or shortened to adjust the clock to get it closer to the 24 hours?
7) Other than the pendulum and spring system we have discussed in class, given an example of where you might encounter simple harmonic motion?
8) A grandfather clock has been calibrated to run perfectly on a midwinter day, i.e. the temperature is approximately 10 degrees C. Will the clock run faster or slower on the summer solstice if the temperature is 20 degrees C? Why?
9) If a spring is oscillating with a frequency of 10 cycles per minute with an amplitude of 5 cm, what is the total energy of the system if the spring constant is 400 N/m?
10) If the total energy of a pendulum system is given as 25 Joules, what is the velocity of 0.1 kg mass at the very bottom of the swing?