Ex. 6: A light spring is stretched by 2 cm when a weight of 10 gm is attached to its free end, the weight is further pulled down by 1 cm and released. Find its frequency and amplitude.
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- 5). The motion of a particle is defined by the follouing equations: ex = x-2y and dt dy =5x-y with x(0)=2 and yco) =-1 dt a. Find x(t) and yit) b. If xlt) and yct) are perniodic, find their amplitudes and peiods. Co which apaph represents the moton best? 3. う人 フイ NIETHER A 2.A uniform stick of length L and mass m is pivoted at one of its ends. Derive an equation for the period of oscillation when the stick is set into small oscillation. Answer in terms of m, g, and L as needed.(a) Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.) (b)Write an equation that represents the curve in the form
- A small steel ball is hanging by a light thread from the ceiling. The steel ball is then displaced 5.0 cm and makes 32 oscillations in exactly 50 s. Determine the period, T, angular frequency, w, and then write the motion of the steel ball as a function of time, t.A uniform thin rod of length 0.714 m is hung from a horizontal nail passing through a small hole in the rod located 0.074 m from the rod's end. The rod is set swinging about the nail at small amplitude. What is the period T of oscillation? T = SThe two blocks shown oscillate on a frictionless surface with a period of 1.5s. The upper block just begins to slip when the amplitude is increased to 40 cm. What is the coefficient of static friction between the two blocks?
- 7. A spring with a spring constant of 55 N/m² is set up horizontally on a frictionless surface with a 3.5 kg mass attached to the spring. If the mass is stretched 0.125 m from equilibrium and released from rest then determine the following:A particle moves in simple harmonic motion with a period of 0.3 s and an amplitude of 6 cm. What are the speed and acceleration of the particle when it is 4 cm from the equilibrium position?