The displacement of a particle varies according to the relation x = 4 (cos wt + sin ît). The amplitude of the particle is: (a) -4 (b) 4√√2 (c) 4 (d) 8
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A: SIMPLE HARMONIC MOTION


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- A 0.15 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by x=(16 cm)cos[(15 rad/s)t + /2 rad] (a) What is the oscillation frequency? (b) What is the maximum speed acquired by the block? (c) At what value of x does this occur? (d) What is the magnitude of the maximum acceleration of the block? (e) At what positive value of x does this occur? (f) What force, applied to the block by the spring, results in the given oscillation? (a) Number Units (b) Number i Units (c) Number i Units (d) Number i Units (e) Number i Units (f) Number i UnitsThe moment of inertia of a physical pendulum of 3 kg oscillating at small angles around an axis at a distance h = 0.8 m from the center of mass is given as I = 1.2 kg m ^ 2. What should be the length of a simple pendulum with a mass of 0.8 kg oscillating in the same period as the small oscillations of the pendulum? bIf the swing amplitude is 0.5 rad, what is the maximum value of the angular acceleration? (a-10rad/S b-20rad/s c-1/10rad/s d-20rad/S). ( figure for first question)A sewing machine needle moves with a rapid oscillatory motion, essentially in simple harmonic motion, as it sews a seam. Suppose the needle moves 9.5 mm from its highest to its lowest position as it makes 36 stiches in 8.0 s. (a) What is the angular frequency, o, of the needle? (b) What is the maximum speed of the needle? (c) What is the magnitude of the maximum acceleration of the needle? (d) Include a diagram of the situation that indicates where the location of the maximum speed and acceleration are located in the motion of the needle. [
- Velocity and Acceleration of Simple Pendulum. L= 1m,T0 = 0, θ = 0, θ’ = 10deg/s, θ’’ = 2deg/s*s. Tf = 1sec, θ = 45 deg, θ’ = 5deg/s, θ’’ = 1 deg/s*s Find the position at T0 and TfThe bob of a simple pendulum is displaced by an initial angle (0) = +Omax/2 and is given an initial velocity in the negative direction. The phase constant. p (in rad), of the angular displacement when expressed as a cosine function isA simple pendulum has a mass of 0.450 kg and a length of 5.00 m. It is displaced through an angle of 13.0° and then released. Using the analysis model of a particle in simple harmonic motion, calculate the following. (Give your answer to the thousandths place.) (b) What is the maximum angular acceleration of the bob?
- The function x- (18 m) cos((Sarad/st a/4 rad) gives the simple harmonic nibtion of a body. Att-76s what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Atsa, what are the le) frequency and )oeriod of the motiont (a) Number UnitsA piston in a gasoline engine oscillates with simple harmonic motion. The displacement of the piston varies according to x(t) = (6.00 cm) cos (2t + ), where x is in cm and t is in seconds. At t= 0, find: i) the position of the particle, ii) its velocity, iii) its acceleration, iv) the period, and v) the amplitude.A simple pendulum has a mass of 0.350 kg and a length of 3.00 m. It is displaced through an angle of 5.0° and then released. Using the analysis model of a particle in simple harmonic motion, calculate the following. (Give your answer to the thousandths place.) (a) What is the maximum speed of the bob? 0.4716 ✔ m/s (b) What is the maximum angular acceleration of the bob? X Your response differs from the correct answer by more than 100%. rad/s² (c) What is the maximum restoring force of the bob? N (d) Solve parts (a)through (c) by using other analysis models. (Hint: you may need to use separate analysis models for each part.) maximum speed maximum angular acceleration maximum restoring force ..(e.).Compare..the.answers. m/s rad/s² N