Question

A manufacturer lists the specifications of a dynamic tensioncompression load cell as follows: - Undamped natural frequency =1000 Hz - Damping ratio =0.707 - Sensitivity =10mV/lbf - Stiffness =100,000lbf/in If the following dynamic force is applied to the load cell, write an algebraic expression for the steady-state output voltage as a function of time. Include the effects of gain and phase response of the load cell. Evaluate all algebraic expressions, leaving only constants, trigonometric functions, and units. F(t)=1000sin(500πt)+500cos(1000πt)+200cos(4000πt)

Answer 1

To write the algebraic expression for the steady-state output voltage of the dynamic tension-compression load cell, consider the effects of both gain and phase response of the load cell. The output voltage can be represented as V(t) = G(ω) [F(t)sin(ωt + φ)], where G(ω) is the gain response, F(t) is the dynamic force applied, ω is the angular frequency, and φ is the phase shift.

Step-by-step explanation:

To write the algebraic expression for the steady-state output voltage of the dynamic tension-compression load cell, we need to consider the effects of both gain and phase response of the load cell. The output voltage can be represented as:

V(t) = G(ω) [F(t)sin(ωt + φ)]

where:

• V(t) is the output voltage as a function of time
• G(ω) is the gain response as a function of angular frequency ω
• F(t) is the dynamic force applied to the load cell
• ω is the angular frequency of the dynamic force
• φ is the phase shift of the load cell

By evaluating the given algebraic expression for the dynamic force, F(t), and substituting it into the equation for V(t), we can calculate the steady-state output voltage as a function of time.