One of the models used for predicting the severity of head injury is shown in Fig. 5.68 where \(f(t)\) denotes the force of blow to the head, \(m_{1}\) is the mass of that part of the head which lies directly under the point of application of \(f(t)\) and moves with \(f(t), m_{2}\) is the rest of the mass of the head, and \(k_{1}\) and \(c_{1}\) are the spring constant and damping constant of the material connecting \(m_{1}\) and \(m_{2}\) in series, and \(c_{2}\) is assumed to be the damping constant contributed by the brain.

a. Derive the equations governing the system.

b. Indicate a procedure for finding the responses of the masses \(m_{1}\) and \(m_{2}\) when \(f(t)\) is an impulse of magnitude \(\bar{f}_{0}\).

Transcribed Image Text:

C2 f(t) m k X3 FIGURE 5.68 Model to predict injury to head. m2