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A mass of 5 kg stretches a spring 10 cm. the mass is acted on by an external force of 10sin(t/2) N (newtons) and moves in a medium that imparts a viscous force of 2 N when the speed of the mass 4 cm/s. if the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/s, formulate the initial value problem describing the most ion of the mass.
a) find the solution of the initial value problem b) identify the transient and steady state parts of the solutionc) plot the graph and the steady state solutiond) if the given external source is replaced by a force of 2 cos wt of frequency w, find the value of w for which the amplitude of the force response is maximum.
A hat contains n coins, f of which are fair and b of which are biased to land on heads with a probability of 2/3. A coin is drawn from the hat and tossed twice.
How many gallons were consumed by each of the two cars that week.
A union strike vote is scheduled for tomorrow, and it looks close. You expect 100 people to vote, and the probability that a typical individual will vote to strike is estimated to be 0.4. Suppose that the voters make their decisions independent from ..
Use the semi-direct product construction to construct a nonabelian group of order pq, where p, q are prime numbers with q = 1 mod p
There are 7 women and 9 men on a faculty. How many ways are there to select a committee of 5 members if at least 1 member must be a woman?
Programmers need to solve systems of equations, which often come up during the design of the games. As an example, suppose in a video game two persons (or objects) are traveling along linear paths
Dotties Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 13 percent of the re..
Definition of a measurable function: the function f is measurable on the interval [a,b] if for all c in R, the set {x in [a,b] : f(x) >c} is measurable.
In each case, sketch the closure of the set: (pi)
A flagpole is n feet tall. On this flag pole we display flags of the following types: red flags that are 1 foot tall, blue flags that are 2 feet tall and green flags that are 2 feet tall.
Given the adjacency relation p = {(1,4), (1,5) (1,6), (6,2), (6,3), (6,5)} on the set N ={1,2,3,4,5,6}, find the corresponding directed graph and adjacency matrix.
The owner of the Rancho Grande has 2972 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions of the largest area..
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