You have just purchased an antique pendulum clock. when you set the pendulum to be of length 100 cm, the clock is 20 % slower than it should be. calculate the length to which you have to set the pendulum for the clock to measure time correctly. (10 marks (b) a mass on a spring oscillates in a simple harmonic motion. at the time t */4s, the diplacement of the mass is i = v3 m, its velocity is v= -1/3 ms and its acceleration is a = -1/3v3) ms? . calculate from these data the amplitude, the angular frequency and the initial phase of this harmonic motion. [20 marks) (c) consider transverse oscillations of a uniform string of length 1.25 m and mass 0.04 kg which is placed under a tension 20 n between its fixed end points. (i) present the equation of motion of this system, (ii) derive the expression for its normal mode frequencies, and (iii) calculate the frequency of its fundamental mode.