4. Given the DE for a spring - mass system: (30 pts) i) Find the solution...
ii please b) For the following DE, do the following: a) Find the solution in phase - amplitude form. If we think of each equation as describing a linear mass-spring system, determine how often the mass crosses the equilibrium position. Find the time at which the mass first crosses the equilibrium position. Estimate the time for which «(1< 1/100 i) "+4x'+8x = 0; x(0) = 1; x'(0) = 2 x"+2x'+10 x = 0; x(0) = 1; x'(0) = 1 4x"+4...
Suppose that a simple spring-mass system can be modeled by the 2nd-order Non- homogeneous ODE stated below. Answer the following questions concerning the properties of this spring-mass system. 4 + 4 = 2 cos(2t); }(0) = 4 (0) = 0 (i) is the spring-mass system an underdamped system, critcally-damped system, overdamped system, or a system with no damping? [Select] (ii) Can this system ever achieve resonance? Select] (iii) is the spring-mass system characterized by the ODE stable? Select] (iv) Does...
solve d ,e , f, g ® Consider a damped unforced mass-spring system with m 1, γ 2, and k 26. a) (2 points) Find if this system is critically damped, underdamped, or overdamped. b) (4 points) Find the position u(t) of the mass at any time t if u(0)-6 and (0) 0. c) (4 points) Find the amplitude R and the phase angle δ for this motion and express u(t) in the form: u(t)-Rcos(wt -)e d) (2 points) Sketch...
3. Consider a system consisting of a Ikg mass connected to a spring with spring co -ION/. and a friction coefficient of 6N/m, subject to an external force of 15 cos 22 newtons). (a) (5 points) Write down the general solution to this system. myll thy't ny=0 "y"+by't loy=0 F(+)= Iscoszt m 2 tlom +10 - (0) (3 points) Label the steady state response and the transient part of the son above (0) (3 points) is the 3 points) Is...
6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey is changed...
a-d please 6 (10) Spring Problems: (a) Find the displacement, y(t), (in arbitrary units) as a function of time for the mass in a mass-spring system described by the differential equatiorn Zy" 10y' + 8y = 100 cos 3t + 4et assuming that the mass is released from rest at the equilibrium position. (This forcing function is not very realistic.) (b) Assume the equation from part (a) describes a mass-spring-dashpot system with a dashpot containing honey. Imagine that the honey...
help me with this Consider the vibration of mass spring system given by the initial value problem m d²x dt2 dx +b. dt + kx = 0 x(0)=0, x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by b2 2m e 2m sin 4mk-b2 4mk 2m t (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release from...
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial value problem dx dx de+b + kx = 0 dt *(0) = 0 . x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by X(t) = 2m Amk- em sin 4mk-02 2m (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release...
Differntial Equations Forced Spring Motion 1. A 1 kg mass is attached to a spring of spring constant k = 4kg/82, The spring-mass system is attached to a machine that supplies an external driving force of f(t) = 4 cos(wt). The systern is started from equilibrium i.e. 2(0) = 0 and z'(0) = 0. There is no damping. (a) Find the position x(t) of the mass as a function of time (b) write your answer in the form r(t)-1 sin(6t)...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...