Question

Which of the following is the correct unit of k in the equation of a damped harmonic oscillator given asЖ
−bv−kx=maб
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 #53352, Physics / Mechanics | Kinematics | Dynamics

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:

Equation of a damped harmonic oscillator:

$$-bv - kx = ma$$

unit of ma is:

$$[ma] = \left[ kg \frac{m}{s^2} \right]$$

therefore unit of kx:

$$[kx] = [ma] = [k][x] = \left[ kg \frac{m}{s^2} \right] = \left[ \frac{kg}{s^2} \right] [m]$$

unit of k is:

$$[k] = \left[ \frac{kg}{s^2} \right]$$

Answer: kgs-2

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