Question

Which of the following is the correct unit of k in the equation of a damped harmonic oscillator given as
−bv−kx=ma
, where b is the damping factor and all the symbols have their usual meaning?


kgms−2

kgs−1

kgms−1

kgs−2

Answer 1

Answer on Question#52047, Physics, Quantum Mechanics

Given the equation of the damped harmonic oscillator $ma = -bv - kx$, we know that each term on the left or on the right of equality sign must have the same dimension. The dimension of $ma$ is $kg \cdot \frac{m}{s^2}$ in SI system.

Since $x$ in $kx$ term has dimension $m$, then if $k$ has unknown dimension $A$, $A \cdot m = kg \cdot \frac{m}{s^2}$, from where the dimension of $k$ is $\frac{kg}{s^2}$ (the last variant from the given list).

http://www.AssignmentExpert.com/