An accelerometer records acceleration for a device that is determined to be equivalent to the function below: a(t) = -1.5 sin(2t)| Given the following initial conditions, x(t = 0) = 0, and v(t = 0) = 1[m/s], determine the position of the device when t = 3.5s.

Page 8/5 Q4: (M4) LE Velocity: V [km/hr] Wavelength: L [m] M k y(t) Model Height: H [m] The figure above shows a model of a person riding a unicycle that contains a spring under its seat. The spring constant is k = 10,600 N/m. Assume that damping is minimal, the wheel of the unicycle has no mass and is not a spring, the unicyle always stays perfectly upright, and the person is represented by a rigid mass M = kg. a) When the unicycle is being ridden at speed V = 10 km/hr over the sinusoidal bumpy terrain shown above, with bump spacing L=0.6 m and bump height H 0.05 m, what will be the steady-state peak-to-peak amplitude of the motion y(t) [m] of the person riding the unicycle? b) Recalculate the steady-state peak-to-peak amplitude of the motion for 2.5, 5, and 20 km/hr. Will the rider have difficulty reaching speeds above 5 km/hr?

汇 Advertised missile performance: Natural Frequency 0.65 a = Angle of attack [rad] q = pitch rate [rad] = 1.25m center of gravity Xcg Zcg = Om center of gravity The equations of motion for the missile are a = q - 0.435sin a + 0.07a -0.00014q q = 111.484(xcg - 1.483)a - (2.2968 - 3.156zcg)q +3.448 + 137895Zcg To acquire the target the missile needs to fly at α = 0.017 [rad] qo= 0 [rad/s] = 0 [rad] So Determine if the missile is stable about the given equilibrium point.

otoring: MITO R (Motor) = VAPPL Torque [N*m] 60 T 0₁ V 200 rad/s W₁ Viscous Friction b₁ N₁ J₁ 2 N₂ b₂ Viscous Friction J₂ VMOTOR K, W₁ T=K₁ i 0₂ ta from the steady state dynamometer test and the given values: J₁ ², b₁ 2N, b2 = 12N, N₁ = 50 teeth, N₂ = 100 teeth (R should rad'

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HW 2_2 The volume of a partially-filled spherical tank can be computed as: V = πα 3 (3R – d); where d is the depth of the water in the tank (m) and R is the radius of the tank (m). Given that R=3m, to what depth must the tank be filled so that it holds 30 m³? Write a PYTHON code & implement the bisection algorithm to answer the question correct to 3 sig figs. Plot to select your own initial guesses. Display the answer in an informative sentence, using formatted printing.

4) Consider the system below. Write the equation of motion and calculate the response assuming that the system is initially at rest for the values k₁ 100[N/m], k2= 100[N/m], k3 = 200[N/m], 100[N/m], k5 = 50[N/m], k6: 50[N/m], and m = = [10kg]. Solve the equation of motion k4 = as a differential equation = F(t) = 80 cos (20t) K5 Κι www K3 ΚΑ m www K6 K2

PLS DO FAST 2 THUMBS UP WILL BE GIVEN THANK U MAKE SURE NOT TO COPY FEOM ELSE WHERE THEY ARE WRONG THX

(b) An object is vibrating with simple harmonic motion (SHM), x(t) = A sinøt of amplitude, A = 15 cm and frequency, f=2 Hz. [Sebuah objek yang bergetar dengan gerakan harmonik mudah, x(t) = A sinot yang amplitud A = 15 cm dan frekuensi, f = 2 Hz.] (i) Determine maximum acceleration and maximum velocity of the vibrating object. [Tentukan pecutan maksimum and halaju maksimum untuk objek bergetar tersebut.] (ii) Calculate the acceleration and velocity for the displacement vibrating object, x(1) = 12 cm. [Kirakan pecutan dan halaju bagi sesaran objek bergetar, x(t) = 12 cm.]

Given a system that has an initial velocity 10 [m/s], at a position of x = 0 [m], determine the time when an object is at a position of x = 40 [m] if its acceleration can be approximated as: Note that: S[√ax ² + b m a(x) = 12 [2] +0.05[1/s²]x +bx+c dx = = ln [2ax + b + 2√a(ax² + bx + c) va