Name:
ME 163 - Mechanical Vibrations
Second Midterm 50 points total, One 8.5 x 11 sheet of notes! Show all your work for full credit By signing your name you agree to the UCSB Honor Code Question 1 (10 pts) Consider the forced vibration system: 2(t)
Lecture 8 We studied the phenomenon of resonance in mass-spring-damper system in the 6th lecture. The key idea was that large amplitude of oscillation can be induced if the external forcing frequency is close to the natural frequency of forcing The f
Lecture 7 Dissipated energy. Forced damped vibration of a linear mass-damper-spring system consists of two parts: the exponetialy decaying part and an oscillatory part. The exponentially decaying part is the homogeneous solution to the forced damped
Lecture 6
Harmonically forced vibrations
In this section we study one of the most important phenomena in science and technology: that or resonance. If it was not for resonance, you would not have stadium rock concerts (might be for the better, I pre
Lecture 5 Example 1 Consider a car, with 1/4 mass m = 500 kg, whose suspension for a single tire has k = 200000N/m. The damping coecient is c = 2000N m/s. A car goes over a bump on the road that gives the suspension system a 6 cm displacement. In how
Lecture 4 Damped free vibrations So far we have been studying systems that have no friction. This is reasonable for a start. Many systems have dynamic properties that are dominated by their inertia, and friction can be neglected at the rst pass. Howe
ME 163 Vibrations Lecture 3 In the second lecture we emphasized the idea that the canonical equation for free undamped vibrations is mx + kx = 0 where m is the mass and k the stiness of the spring-mass system. We introduced various changes of coordi
ME 163 Vibrations Lecture 2 We are going to consider a couple of examples where the equations of motion -these are second order ordinary dierential equations that we derive using Newtonian mechanics - can be reduced to the above analyzed canonical fo
ME 163 Vibrations Lecture 1 Why study vibrations? In engineering, most commonly we want to suppress them. Although, as the video shown in class indicates, we can use our knowledge to produce some unusual eects with cars. You wouldnt want to buy a car
Lecture 10 0.1 Accelerometer
The story we talked about last time was that of vertical support motion, the kind that occurs in earthquakes. Typical highest natural frequency of building motion is 1/10th of a Hertz, so short-duration earthquakes typic
Lecture 11 0.1 Forced response
Very often, the force input into a spring-damper-mass system is not periodic. The earthquake vibration of the ground is not, and neither is the force that stresses your cell phone when it hits the ground. We do not lik
Name:
ME 163 - Mechanical Vibrations
First Midterm 50 points total, One 8.5 x 11 sheet of notes! Show all your work for full credit By signing your name you agree to the UCSB Honor Code Question 1 (17pts): Consider the dierential equation of motion
Lecture 17: Lagrangian Mechanics We use the approach of Lagrangian mechanics to provide an easy way of deriving equations of motions for complicated interconnected systems. All we need to know to use this approach is the kinetic energy T of the syste
Lecture 15: Forced vibrations, 2-DOF systems 0.1 Matrix methods for 2-DOF system with forcing
We have seen how matrix methods simplify analysis for free vibration of 2-DOF. Now we use those to enable analysis of forced systems. We will see how the u
Lecture 14
1
Matrix mechanics
In this lecture we will use matrix algebra to the full extent. The matrix version of equations of motion for the system shown in gure ? is m0 0 2m x1 2k k = x2 k 2k x1 x2
Thus, using our denition of the mass matrix
Lecture 13
1
State space (phase space) view of 1 DOF systems
So far we have concentrated mostly on understanding of time dependence of the response - position, velocity or acceleration - of a vibration system to excitation. The excitation was eith
Lecture 12 0.1 Shock response
One of the typical vibration engineering design tasks involves protecting a device from a shock impulse, such as when one drops a cell phone on the oor. A more extreme example is that of a torpedo hitting a ship whose b
ME163 Mechanical Vibrations (Winter 2009) Due Wednesday 2.4.09 7pm (in the box or to a TA) Worth 75 Extra Credit points Answers emailed by 9pm, midterm the day after 1. Consider the system in gure below, with mef f = 20 [kg], damping coecient c = 500
ME163 Mechanical Vibrations (Winter 2009) HW-3 Due 1.29.09 in class -25% if late within 24 hours -50% if later than that 1. This problem aims to give you a avor into the process of designing cars for an adventurous roller coaster ride. We can model t
ME163 Mechanical Vibrations (Winter 2009) HW-2 Due 1.22.09 in class -25% if late within 24 hours -50% if later than that 1. In order to experimentally determine the stiness and damping coecient of the system below, a bump test is performed. A bump te
ME163 Mechanical Vibrations (Winter 2009) HW-2 Due 1.22.09 in class -25% if late within 24 hours -50% if later than that 1. In order to experimentally determine the stiness and damping coecient of the system below, a bump test is performed. A bump te
ME163 Mechanical Vibrations (Winter 2009) HW-1 Due 1.15.08 in class -25% if late within 24 hours -50% if later than that 1. This problem is a review of some necessary background from mathematics. Consider the following dierential equation x(t) + 2x(t
ME163 Mechanical Vibrations (Winter 2009) HW-1 Due 1.15.08 in class -25% if late within 24 hours -50% if later than that 1. This problem is a review of some necessary background from mathematics. Consider the following dierential equation x(t) + 2x(t
ME163 Mechanical Vibrations (Winter 2009) Due Wednesday 2.4.09 7pm (in the box or to a TA) Worth 75 Extra Credit points Answers emailed by 9pm, midterm the day after 1. Consider the system in gure below, with mef f = 20 [kg], damping coecient c = 500
ME163 Mechanical Vibrations (Winter 2009) HW-3 Due 1.29.09 in class -25% if late within 24 hours -50% if later than that 1. This problem aims to give you a avor into the process of designing cars for an adventurous roller coaster ride. We can model t
ME163 Mechanical Vibrations (Winter 2009) HW-5 Due 2.12.09 in class -25% if late within 24 hours -50% if later than that 1. Forced Vibration, The Complete Solution. Consider the direct forced vibration system: x + 0.5x + 25x = 1.55 sin(8t) (a) Deri