The function that describes this oscillation in time is of the form Y (t) = eat (2 cos(bt) + sin(bt)), where x a + bi is the solution with b > 0 to the following equation mx + rx+ k = 0. In this equation, m represents the mass in kg, k is the spring constant and measures the spring's elasticity, r measures the friction damping effects. (a) Suppose the mass weighs 10 kg, the spring constant k is 2 and r is 4. Find a and b by solving the quadratic equation. (b) Substitute a and b in the expression for Y(t). (c) Find the initial extension of the spring A = Y(0).

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.