Question: The spring actuator shown in Fig. 3.42 operates by using the air pressure from a pneumatic controller ( p) as input and providing an output

The spring actuator shown in Fig. 3.42 operates by using the air pressure from a pneumatic controller ( p) as input and providing an output displacement to a valve (x) proportional to the input air pressure. The diaphragm, made of a fabric-base rubber, has an area A and deflects under the input air pressure against a spring of stiffness k. Find the response of the valve under a harmonically fluctuating input air pressure p1t2 = p0 sin vt for the following data: p0 = 65 kPa, v = 8 rad/s, A = 0.065

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