f a person increases how fast they are shaking a spring up and down, what characteristics of the wave change? What characteristics of the wave stay the same? Why?
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- 1. a) What effect does increasing the mass on the end of a string have on the period of a pendulum? b) What effect does increasing the length of the string have on the period of a pendulum? c) What effect would moving to a location with a smaller acceleration due to gravity have on the gravity have on the period of a pendulum?3. Two balls of mass are connected to each other and to the wall by two springs as shown in figure. Use the mass values of the balls and spring constant values of the springs given in the figure, to obtain (a) the equations of motion, (b) the normal frequencies, and (c) the amplitude ratios of the normal vibrations. 2k ooooo 2m k ooooo m16) A block attached to an ideal spring of force constant (spring constant) 15 N/m executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s2 . The mass of the block is closest to A) 2.3 kg B) 2.6 kg C) 4.7 kg D) 9.4 kg Answer: C
- . Astronauts on a distant planet set up a simple pendulum of length 1.2 m. The pendulum executes simple harmonic motion and makes 100 complete oscillations in 280 s. Determine the ff: a) frequency b) period c) acceleration due to gravity13. A particle is released from rest at a distance 4m from the origin and moves in simple harmonic motion according to the equation x" = -102x (a) What is the period of the motion? (Ъ) What is the maximum speed of the particle?24) A fan unit in a furnace is oscillating up and down. The simple harmonic motion can be described as having a period of 0.17 s and a range (from the maximum in one direction to the maximum in the other) of 0.61 mm. At t = 0 it is at its central position and moving in the -y direction. When t = 0.02 s on the stopwatch, where is the unit? a) y = -0.11 mm b) y = -0.22 mm c) y = -0.44 mm d) y = 0.21 mm e) y = -9.03 mm
- *48. CD Multiple-Concept Example 11 explores the concepts that are important in this problem. Pendulum A is a physical pendulum made from a thin, rigid, and uniform rod whose length is d. One end of this rod is attached to the ceiling by a frictionless hinge, so the rod is free to swing back and forth. Pendulum B is a simple pendulum whose length is also d. Obtain the ratio T/T of their periods for small-angle oscillations.3. This problem is about driven oscillating systems. As we saw in lecture, when a mass-spring system is set in motion (given a tug or a kick) and subsequently left alone, it will oscillate at a frequency that depends on the spring constant and the mass, which is called the natural frequency, wo = However, what if an additional sinusoidal force with arbitrary TTL frequency w is applied? a) Consider a horizontal mass-spring system with an additional horizontal driving force F = Focos (wt) where Fo is a constant. For now, assume wwo. Using Newton's second law, find a differential equation for the position of the mass. b) To solve the differential equation from part a), try a solution with the form x = A cos (wt) where A is a constant. What must A be to solve the differential equation? c) The solution given in part b) shows that the mass can oscillate at the frequency of the driving force instead of its natural frequency. However, notice that the solution in part b) has no arbitrary…