Question

2. The position of the motion of the bob in a simple pendulum in radians is given by 0(t)-3cos What is the amplitude, frequency, and period of the motion? 3.A man enters a tall tower needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor, and its period is 12 s. How tall is the tower? Two playground swings start out together. After 5 complete oscillations, the swings are out of step by half a cycle. If the time it takes for one swing to complete 10 oscillations is 2 minutes 5. A pendulum with a swing amplitude of 5° is known to have a period of 5 s. What is the 6. A ride at six flags straps you in and you swing like a pendulum. The length of the cord that 7. The position of a 0.5 kg object attached to a spring is described by the equation: what is the difference in the heights of the swings? length of the pendulum's string? hold you is about 20 m. How long does it take to swing back and forth thrice? x(t)-(5 m) cos(2π t). What is the spring constant? 8. A spring stretches 3 em when a 5 g object is hung from it. The object is replaced with a block of mass 50 g which oscillates in simple harmonic motion. What is the period of the motion? 9. It is known that a load with a mass of 25 g will stretch a spring 5 em. The spring is stretched an additional 30 em, and then released. (a) What is the spring's constant? (b) What is the period and frequency of the oscillations? 10. How would you determine the mass of an object on the space station in space?

Answer 1

(2) The equation of position of the motion an be written as :

$\theta(t) = A*cox(kx + wt)$

thus comparing with the given equation:

Amplitude A = 3

Frequency w = $\pi$ = 2$\pi$f

f =1/2

Period of Motion f = 1/T = =1/2

T = 2