3 a): foot above the equilibrium position with a downward velocity of 14 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1
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- 3) A 5 kg mass is attached to a spring with spring constant k = 100 N/m, and moves along a horizontal surface which produces a resistive force R = -bv where b = 8 N/m/s. a. Calculate what the angular frequency o would be if there were no resistive force/damping. Is the damped angular frequency greater of less than this? b. Calculate the damping constant a, and what type of damped motion (under critical or over critical damped) occurs? c. Calculate the actuals (damped) angular frequency of the motion. d. The position of the object at any time is x(t) = e-at [Pcos (wot) + Qsin(wot)], where P and Q are constants. Differentiate this to obtain its velocity at any time. f. e. If the object is released from rest at 1 = 0 at position xo = 0.1 m, find the values of P and Q. Convert your solution to the form x(t) = Ae-at cos(wot-d) by finding the values of A and from P and Q. How long does it take the mass to reach the equilibrium point (x = 0) for the first time? g. Differentiate your solution…3 c) A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 14 ft/s. What is the position (in feet) of the mass at the instant that you found in 3(b.) Round your answer to four digits after the decimal sign.A mass weighing 1 lb is attached to a spring whose spring constant is 1.5 lb/ft. The medium offers a damping force that is numerically double the instantaneous velocity. The mass is released from a point 10 cm above the equilibrium position with a downward velocity of 2.3 m/s, Determine: 1. Time it takes for the object to pass through the equilibrium position. 2. Time in which the object reaches its extreme displacement from the equilibrium position. 3. What is the position of the mass at the instant calculated in part 2? 4. Graph the movement.
- An object of mass of 2.0 kg hangs from an ideal massless spring with a spring constant of 50 N/m.An oscillating force F = (4.8 N) cos[(3.0 rad/s)t] is applied to the object. What is the amplitude of theresulting oscillations? You can neglect damping.A) 0.15 m B) 2.4 m C) 0.30 m D) 0.80 m E) 1.6 m8. A weight of 0.5kg stretches a spring by 0.49m. The spring-mass system is submerged in delicious melted butter with a damping coefficient of y=4. The spring is then lowered by an additional 1.0m and released with velocity 0. There is no external force. Find the function which gives the location of the weight at time t. Note: I have designed this to work out nicely. If it's not working out nicely then you probably got some butter in your calculations.7a You are on a fishing trip, not catching anything, and bored - time for physics! You drop your 50g weight to the bottom of the lake under constant tension from the string of magnitude 0.1N. The damping constant for your falling weight is 2.5kg/s. What is the terminal velocity of the weight? Give your answer in m/s and assume the positive direction is upwards b If it takes 500s for the weight to reach the bottom of the lake, how deep is the lake? Give your answer in m.
- A small insect of mass 0.25 g is caught in a spider's web. The web oscillates predominantly with a frequency of 2.70 Hz. What is the value of the effective spring stiffness constant k (in N/m) for the web? Type your answer correct to within two decimal places. Use a period (full stop) for a decimal place, eg. 500.00 - Do not use a comma or input your answer in some form of scientific notation. Do NOT include units in your answer. Type your answer.weight .) A weight of 64 pounds (Recall mx" + Bx' + kx stretches a spring 2 feet. A damping device imparts a damping force 0 and m 32 numerically equal to 16 times the instantaneous velocity. The initial position is x (0) = 2 and the initial velocity is x' (0) = –1 . This is the equation of motion for the mass. -4t x = (-2t – 1) e t -4t O x = (-7t – 2) eAt -2t O x = 2e cos(2t) +e t sin(2t) -4t O x = (7t + 2) eA linear second order, single degree of freedom system has a mass of 8 x 103 kg and a stiffness of 1000 N /m. Calculate the natural frequency of the system. Determine the damping coefficient necessary to just prevent overshoot in response to a step input.
- Damped Oscillator Consider a 5. weakly damped oscillator with B < wo. There is a little difficulty defining the "period" Ti since the motion is not periodic However, a definition that makes sense is that T1 is the time between successive maxima of r(t) (a) Make a sketch of x(t) against t and indicate this definition of T1 on your graph. Show that T1 27T/w1 (b) Show that an zeros of xt). Show this one on your sketch. (c) If B = wo/2, by what factor does the amplitude shrink in one period? equivalent definition is that Ti is twice the time between successive 11An automobile suspension system is critically damped, and its period of free oscillation with no damping is 1 s. If the system is initially displaced by an amount and released with zero initial velocity (at t = 0; x(0) =x, and v(0) = 0) %3D a- Determine the value of the angular frequency of free oscillation with no damping. (wo = ??) b- Deduce the value of friction factor (g =??) c- Write the expression of position as a function of time of the system, if the system is critically damped. (x(1) = ??) d- Deduce the expression of the velocity of the system. (v(t) = ??)A 6-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 30 N/m and the damping constant is 3 N-sec/m. At time t=0, an external force of 2 sin 3t cos 3t N is applied to the system. Determine the amplitude and frequency of the steady-state solution. **..*. Using g= 9.8 m/sec", the equilibrium displacement of the mass is (Type an integer or a decimal.)