1) let h1[n] be the impulse response of a causal type ii fir generalized linear phase system. let h2[n] = δ[n] − δ[n − 1] be the impulse response of another lti system. let t be a lti system with impulse response given by the convolution h[n] = h1[n] ∗ h2[n]. a) prove that t is a generalized linear phase system. b) what type (i, ii, iii or iv) of generalized linear phase system is t? explain your answer. 2) the impulse response of a discrete-time lti system t is h[n] = c1δ[n] + c2δ[n − 1] − c2δ[n − 3] − c1δ[n − 4] where c1 and c2 are real positive constants.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.