QI (a) Evaluate equation y" - 3y' - 4y = e* using the Laplace transform, with initial conditions y(0) = -5 and y’(0) = -1. (b) Figure Q1(b) shows a mass of 5kg, in a water tank, is connected with a spring. The mass is pulled down as far as x with an initial Force of Fo = 4N. The spring coefficient and the damping coefficient are known, k = 10N/m and b = 15kg/s, respectively (i) Derive the empirical equation of the homogeneous solution (ii) Compute the homogeneous solution if initial conditions are given, y(0) = 1 and y'(0) = -7. (iii) If the function of Force at particular time is given as F(t) = F, sin wžt. Determine the particular solution. (iv) Evaluate the General equation of non-homogeneous solution. Note that F = m a, and wo =

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.