Write the equation for the general motion.

Which one of the following equations is dimensionally homogeneous? Show your proof. F(x, – 4,) =m; -mv; 1 а. 1 b. F 1 c. F(V,-v,)==m; --mx 1 d. F(t, -4)= mV, – mV, where F = force (N) %3D x= distance (m) m= mass (kg) V = velocity (m/s) t = time (s)

"A seismograph detects vibrations caused by seismic movements. To model this system, it is assumed that the structure undergoes a vibration with a known amplitude band frequency w (rad/s), such that its vertical displacement is given by xB=bsin(wt). This movement of the structure will produce a relative acceleration in the mass m of 2 kg, whose displacement 2 will be plotted on a roller." x= 15 kN/m Structure -WI 24 mm (Ctrl) sin(wt) b(w/w)² √√1 (w/w)] + [25(w/w)]²' "The seismograph's roller measures 60 mm, and a maximum vibration amplitude of the structure of b<5 mm is expected. Design the damper (constant c) to ensure that, for a constant oscillation, the seismograph functions correctly and the needle does not move off the roller."

For the following problem please show your step by step process so your thought process can be followed. Please also show a sketch, quantities given, quantities to be found, and boxed answer with units.

Damian’s car weighs 2000kg. The spring has a natural unstretched length of 2m and a spring constant of k = 80000N/m.  Hooke's law can be written as T = kd. Where T is the tension force in newtons, k is the spring constant and d is the length in metres. Let x(t) be the position of the front of Damian’s car and let y(t) be the position of the back of Eva’s 4WD. We will assume that the position of Eva’s car is a known function of time. Q1 a) Create a sketch of the positions of the vehicles similar to the one given and add the positions x and y. b) What is the extension of the spring in terms of x(t) and y(t)? Be careful to take into account that the unstretched length of the spring is 2m.

When a 5000 lb car driven at 60 mph on a level road is suddenly put into neutral gear (i.e. allowed to coast), the velocity decreases in the following manner: 60 V = mph , 1+() where t is the time in sec. Find the horsepower required to drive this car at 30 mph on the same road. Useful constants: 9 = 22 mph/sec, 1 H.P. = 550 ft.lb/sec, 60 mph = 88 ft/sec.

A 5-kg object is acted upon by a horizontal force P=18t [N], where t is time in seconds. The coefficient of kinetic friction is µk = 0.15. At t = 2 s, the object's velocity is 10 m/s. Determine the velocity at t = 4 s. Use the Impulse-Momentum method. Provide the free-body diagram and show all work. P

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2. What is the equivalent stiffness of the system of Fig. 1-19 using the displacement of the block as the generalized coordinate? E = 210 x 10 x 10ʻ N 1= 1.5 x 10 mª 2.5 m 2 x 10 N 3 x 10 N Fig. 1-19 Answer: 4,690,000 N/M

A 1.2 kg object is oscillating in simple harmonic motion at the end of an ideal horizontal spring ir the frictionless air track. Its position as a function of time t is given by r(t) = (0.045 m)cos[(15 rad/s)t - /8). a) What is the spring constant? k= N/m b) What are the frequency and period of the oscillation? f= Hz T= c) What is the maximum speed that the object reaches? vmax= m/s What is the particle's position when the velocity is maximum? d) What is the maximum acceleration that the object reaches? amax= m/s? What is the particle's position when the acceleration is maximum? e) What is the maximum energy of the system? KE= J f) Find the acceleration of the object when the object is at x=0.025 m. m/s2 a=