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 #51849, 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

$$- b v - k x = m a,$$

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:

$$- b v - k x = m a$$

unit of ma is:

$$[ m a ] = \left[ k g \frac {m}{s ^ {2}} \right]$$

therefore unit of kx:

$$[ k x ] = [ m a ] = [ k ] [ x ] = \left[ k g \frac {m}{s ^ {2}} \right] = \left[ \frac {k g}{s ^ {2}} \right] [ m ]$$

unit of k is:

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

Answer: kgs-2

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