TASK 1 - Modelling, matrices, MATLAB loops, eig

Consider an n-degree-of-freedom undamped mass-spring system shown. Assume that the following parameters of the system are known and given: n = 200; m1 = m2 = m3 = ... = m200 = 5[kg]; k1 = k2 = k3 = ... = k200 = 1000 [N/m]. Find numerical value of the 7^th natural frequency omega_7 [rad/s] of the system. (Round your result up to two digits after the dot and find the best match with the answers presented).

1.33 rad/s

1.44 rad/s

1.55 rad/s

1.77 rad/s

4.52 rad/s

sqrt(1000/5) = 14.14 rad/s

0.28 Hz

None of the above

I could not complete this Task.

TASK 2 - 1st Order Ordinary Differential Equations, Newton's Law of Cooling, MATLAB

You are given a hot sample of metal with initial temperature T0 equal to 192 deg C. You leave the metal in a thermal chamber, where after four minutes it has cooled to 80 deg C. What was the surrounding temperature in the chamber?

Program simulation of this task in a single MATLAB file, using anonymous function and ode45 solver. Simulate cooling process during 5 minutes, for the following conditions: T0 = 192; k = -0.293893; values of Ts = [15 20 25 30 35 40 45 50] and determine which particular value out of these eight values of temperatures corresponds to the condition of the task, i.e. cooling to 80 deg C after 4 minutes.

15

20

25

30

35

40

45

50

None of the above

TASK 3 - Projectile motion, ODE, MATLAB, interp1

A tennis player is hitting a ball exactly at the centre of the baseline at the height H = 2.31 m and is launching the ball at the negative angle of -3.5 degrees with respect to the horizon with the speed of v = 206 km/h in the vertical (i.e. orthogonal to the ground) plane, parallel to the centre service line, as shown in Figure (attached). The ball is flying over the "centre service line".

(1) Determine the instantaneous radius R (in m) of the ball's trajectory at initial time of the serve, i.e. at t=0. YOUR TASK-2(1) ANSWER R [in m]:

27.40

114.40

224.40

334.40

574.40

1354.40

none of the above

I was unable to complete this question

(2) Treating tennis ball as a point and assuming NO AIR DRAG, use MATLAB to determine time "t_land" when the ball hits the ground. [Assume that the absolute value of the gravity acceleration is equal to 9.81 m/s².] Present result in seconds [type in the window below numerical figure only], rounded to two digits after the dot. Hint: you may wish to use "ode45" to solve projectile task numerically, then use "interp1" on solution data to determine time when ball is hitting the ground.

(3) Using results from (1) and "interp1" command, determine horizontal distance "x_land" traveled by the ball before it hits the ground. Present result in meters, rounded to two digits after the dot. [With this answer you will know if the ball was IN or OUT].

(4) Using results from (1) and "interp1" command, determine vertical height "z_inNet_plane" of the trajectory of the ball [i.e. vertical distance from the ground to the ball] at the instant when the ball is in the vertical plane of the net. Present result in meters, rounded to two digits after the dot. 'With this answer you will know if the ball hit the net or not: the net is 0.91 meters high in the center].

TASK 4 - Projectile motion: linear versus non-linear model, coordinate systems, ODE, MATLAB, interp1

During the experiment, mass m = 1 kg was released and travelled distance AB = h before it hit the inclined flat surface, as shown in Figure.

Assume the following parameters of the experiment: inclination angle v = 30^o; h = 2m and

1. Determine the distance BC = d and travel times t_AB and t_BC numerically, formulating and solving the associated differential equations of motion for the mass m, assuming NO air resistance;

2. Determine the distance BC = d, and travel times t_AB and t_BC numerically, formulating and salving the associated differential equations of motion for the mass m, assuming that the air resistance force is proportional to the product of the squared velocity of the mass and coefficient C_d = 0.8:

F = C_d x v²

YOUR TASK - 4.1a ANSWER for BC = d [in m]: (No air resistance case)

3 m

5 m

8 m

9 m

11.5 m

None of the above

YOUR TASK - 4.1 b ANSWER for t_AB [in s]: (No air resistance case)

0.52 s

0.64 s

0.93 s

 1.71 s

None of the above

YOUR TASK - 4.1 c ANSWER for t_BC [in s]: (No air resistance case)

0.73 s

1.09s

1.27s

1.85 s

2.39 s

None of the above

YOUR TASK - 4.2a ANSWER for BC = d [in m]: (Air resistance case!)

0.81 m

1.19 m

3.27 m

4.92 m

5.67 m

None of the above

YOUR TASK - 4.2b ANSWER for t_AB [in s]: (Air resistance case!)

0.51 s

0.71 s

0.81 s

2.51 s

None of the above

YOUR TASK - 4.2c ANSWER for t_BC [in s]: (Air resistance case!)

0.58 s

0.84 s

2.24 s

4.34 s

None of the above

Attachment:- Assignment File.rar