A particle executes simple harmonic motion of amplitude A along the X-axis. At t- 0, the position of the particle is x- A/2 and it moves along the positive x-direction. Find the phase constant & if the equation is written as *- A sin(wt + 8).
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- A physical pendulum composed of a solid sphere with radius R = 0.500m, is hanged from a ceiling by string of length equal to radius. What are the (a) angular frequency, (b) period, (c) frequency of the systemfor small angles of oscillation? For solid sphere Icm = 2/5 mr2.For a simple harmonic oscillator with x=Asinωt write down an expression for the velocity.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 damped SHO has spring constant, k=10 N/m, mass, m=1 kg and friction constant, b=2kg/s. What is the frequency of the oscillations?A particle oscillates according to x = Acos(ωt + δ) Determine the phase constant δ if the particle starts from x0 = −A.For a simple harmonic oscillator with x = A sin ot write down an expression for the magnitude of acceleration. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes). For power (e.g. A2) use A^2 or A*A. For trigonometric functions use the usual sin and cos, while for Greek letters such as w, use omega. Please use the "Display response" button to check you entered the answer you expect. a= Display response
- What is the phase constant (from 0 to 2π rad) for the harmonic oscillator with the velocity function v(t) given in the figure if the position function x(t) has the form x = xmcos(wt + p)? The vertical axis scale is set by vs = 5.00cm/s. Number 1.57 v (cm/s) -15 Units radAsap plzFor a simple harmonic oscillator with x=Asinωtx=Asinωt write down an expression for the velocity. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes). For trigonometric functions use the usual sin and cos, while for Greek letters such as ωω, use omega.
- A particle moves along X-axis according in the equation x = a sin wt + b cos ot, where a, b and o are constants. Show that the motion is S.H.M. Further, if a = 3 cm, b = 4 and o %3D 5 rad/s, find (1) amplitude, (2) period and (3) initial phase.A mass on a spring is held at a distance of 0.05 m from the equalibrium position. It is then released at time t=0 and undergoes simple harmonic motion. If the mass was 0.2 kg and the spring constant k was 6 Nm-1, what is the velocity of the mass at time = 7 seconds?At what positions is the speed of a simple harmonic oscillator half its maximum? That is, what values of x / X give v = ±vmax / 2 , where X is the amplitude of the motion?