5. The position of a SHM as a function of time is given by x = 3.8 cos (5nt/4 +n/6) where t is in seconds and x is in meters. Find: (a) the period and frequency (b) the position and velocity at t= 0 s, (c) the velocity and acceleration at t 2.0 s
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- What frequency is depicted in the following equation of an oscillator? Assume that the units work out and the amplitude is in millimeters and the time tt is in seconds. x(t)=−2.2sin(40t−π3)x(t)=−2.2sin(40t−π3) a. 6Hz6Hz b. 20πHz20πHz c. 16Hz16Hz d. 180πHz180πHz e. π20Hzπ20Hz f. 80πHz80πHz2. A 1 kg mass is attached to a spring and executes SHM with a position given by: x(t) = (2m/s)cos[(πrad/s)t − 3π/2] (a) What is the period? (b) What is the amplitude? (c) What is the maximum velocity of the mass?(d) What is the maximum acceleration of the mass? (e) What is the force constant of the spring? (f) What is the position of the mass at t=0? (g) What is the position of the mass at t=1 s? What is the velocity at t = 1s? (h) What is the total energy of the system at t =1 s?2. The length of a simple pendulum is 0.66 m, the pendulum bob has a mass of 310 g, and it is released at an angle of 12º to the vertical a. With what frequency does it oscillate? Assume SHM.
- 10:24 0. Shop O O 7 l 87% i AIATS For Two Year Medic. A (02:59 hr min 1 /180 Mark for Review If a SHM is given by equation y = (sinrt +cost) m, then which of the following statements is correct? The amplitude of oscillation is 1 m The amplitude of oscillation is 2 m Particle starts its motion from y = 0 m The period of oscillation is 1 second Clear Response II III8. A mass on a spring oscillates along a vertical line, taking 12 s to complete 10 oscillations. a. Calculate (i) its period (ii) its angular frequency b. Its height above the floor varies from a minimum of 1.00 m to a maximum of 1.40 m. Calculate (i) its amplitude (ii) its maximum velocity (iii) its acceleration when it is at its lowest position.. A mass is placed on a frictionless, horizontal table. A spring (k=99 N/m) which can be stretched or compressed, is placed on the table. A 6 kg mass is attached to one end of the spring, the other end is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x= 3 cm and releases it from rest. The mass oscillates in SHM. (a) Determine the equations of motion in terms of the amplitude 'A', the angular velocity 'w', and the time 't'. Use the initial conditions to find the value of in the equations. Hint: Use the equation editor (orange button in the answer box) and find w in the greek letters. DO NOT USE numerical values for A and @ for part (a). For example, a equation could be x(t)= Asin (wt). x(t)= m v(t)= a(t)= m/s m/s² (b) Calculate for this spring-mass system. @= rad/ s (c) Find the position, velocity, and acceleration of the mass at time t=2.8 s. Use @ up to 4 significant figures in the calculation. Note: Should you set your calculator in…
- The motion of a body attached to a vertical oscillating spring is given by the equation: y(t) = 4.75 sin (0.800 ? t) The time variable, t, is in seconds and the displacement variable, y, is in meters. Find a) the amplitude; b) the period; c) the frequency: d) the displacement at 1= 3.00 sec: e) the displacement at t= 8.00 sec3. A mass on a spring moving along the x-axis in simple harmonic motion starts from the equilibrium position, the origin, at t = 0 and moves to the right (consider the right to be the positive x direction). The amplitude of its motion is 3.00 cm and the frequency is 1.50 Hz. At what earliest time does this mass have the maximum positive acceleration (i.e.pointing in the positive x direction)? X = 0 +x a. t= 0.500 seconds. b. t= 0.667 seconds. Ax с. t = = 1.50 seconds. d. t= 0.167 seconds. e. t= 0.314 seconds.The position of a Simple Harmonic Oscillator based on time is given by x-3.8 cos(5o/4.t+π/6) where t is in seconds and x in meters. Find a) maximum speed and b) maximum acceleration, and c) speed and acceleration at t-0 sec.