A simple pendulum, which has been given a small displacement, will perform simple harmonic motion. The time period T of the resulting oscillations is given by T = 2π p l/g, where l is the length of the pendulum and g is the gravitational field strength (g = 9.8 m s−2 ). Consider two pendulums with lengths l1 and l2. Express their periods T1 and T2 in terms of l1 and l2. Find the ratio l1/l2, if it is given that the first pendulum swings back and forth 10 times per minute, while the second one swings back and forth 300 times per hour.

A frictionless pendulum of mass m=1 kg and length L=1 m, gets released at t=0 from a distance x=0.12 m relative to its equilibrium position. м M What is the velocity of the pendulum's mass at time t=1.5 s? Give your answer in units of [m/s] and up to 1 decimal place (e.g. 0.6)

A mass on the end of a spring oscillates with an amplitude of 35cm at a frequency of 20 Hz (cycles per second). At t = 0 the mass is at its equilibrium position (x = 0). a) Find the possible equations describing the position of the mass as a function of time, in the form x = A cos (ωt + φ), giving the numerical values of A, ꞷ and φ. b) What are the values of x, dx/dt, and d2x/dt2 at t = 3⁄4 sec?

The oscillatory movement of a simple pendulum is a characteristic of the regular repetition of displacements around an equilibrium position. The pendulum swings due to the restored force of gravity, which seeks to bring the mass back to the equilibrium point. The oscillatory behavior is described by a trigonometric solution, which relates the pendulum's position to time, considering its amplitude, frequency and initial phase. Statement: A simple pendulum moves according to the following question:y(t) = A.sin(ωt + φ)In this question, y(t) is the horizontal position of the pendulum, A is its amplitude, ω is its angular velocity, given by ω = 2πf, and φ is the initial phase of the movement, in radians. Since the initial phase of the movement is equal to 0 and its angular velocity is π/2 rad/s, the oscillation frequency of this pendulum is correctly given by the alternative: a) 2.0Hz b) 1.5Hz c) 1.0Hz d) 0.5Hz e) 0.25Hz