(a) Amplitude has dimensions of length and its mks unit is meter.
Frequency has dimension 1/T and its unit is sec-1
(b) Velocity =
as the unit of velocity is m/s, The coefficient A has the units of m/s as the sine function is dimensionless
(c)
as the unit of accleration is m/s2, The coefficient A2 has the units of m/s2 as the cos function is dimensionless
A particle undergoes simple harmonic motion (SHM) in one dimension. The r coordinate of the particle...
The displacement of the particles of a string in a SHM ( simple Harmonic motion ) is a cosine function of time X = 0.04 Cos (376.8 t ) 0.04 is in meters. Find the following. You must write the symbol, and also unit for each quantity. a) Amplitude of the string particles b)) angular frequency, b) Frequency, c) Period d) Displacement of the vibrating particles of the string at t= 2 seconds e) Maximum velocity of the vibrating...
The equation of motion of a particle undergoing simple harmonic motion is x=4.00sin0.500t, where x is in centimeters. At t=1.00 s, determine the particle's displacement, velocity, and acceleration.
A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 3.50cm, and the frequency is 2.30 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.) x...
The position function of a particle undergoing Simple Harmonic Motion is given below: D. 2 = 5 sin (36), where x is in m, and t is in s. Round your answers to the nearest tenth. Do not include units in your answers. (1) What is the particle's period of motion, in s, ? (2) Where will the particle be at t=3s, in m, ? (3) How fast will the particle move at t=1 s, in m/s, ? (4) What...
In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 7.00 cos (4t + ) where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. 6.30 cm (b) At t = 0, find velocity of the piston. -9.11 How do you find the velocity v(t) of an object if you know the position as a function of time,...
Check my work Problem 19.002 - Frequency and velocity of a particle in simple harmonic motion A particle moves in simple harmonic motion. Knowing that the amplitude is 0.24 in, and the maximum acceleration is 225 ft/s, determine the maximum velocity of the particle and the frequency of its motion. points (8 03:40:34 The maximum velocity of the particle is ft/s, and the frequency of its motion is Hz. eBook Hint Print References
A piston executes simple harmonic motion with an amplitude of 0.1 m. If it passes through the center of its motion with a speed of 0.5 m/s, what is the period of oscillation? 20 pts Problem 3.2 Use the general expression for r(t) for Simple Harmonic Motion (SHM) Express the period To as a function of wo The amplitude of the motion is given, so just take the first time derivative of the displace- ment and compare with the velocity...
A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t0 and moves to the right. The amplitude of its motion is 2.50 cm, and the frequency is 2.90 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.) x2.5sin (5.8xt)...
A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is2.50 cm, and the frequency is 1.30 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t, and ?.) x = (b) Determine the maximum speed of the particle. cm/s (c) Determine the earliest time (t...
A particle undergoes simple harmonic motion with amplitude 25 cm and maximum speed 4.8 m/s. If a stopwatch is started when the particle is pulled to its maximum position and released, what is the formula for the position of the particle as a function of time?