A simple pendulum is shown on the right. For this simple pendulum, use dimensional analysis to decide which of the following equations for can be correct.

Which of the following is correct? How can you tell?

A stationary block of mass m, lying on a horizontal frictionless surface, is attached to a horizontal spring. The block is pulled 10 cm to the right (+ direction) and released. You start your stop watch as the block passes through its equilibrium position for the first time. Which curve given above best represents the motion of the block?

1. If the frequency of oscillation of the block is 2 Hz, what is the approximate position of the block after 1.45 s? (a) 0 cm (b) -10 cm (c) 0.6 cm (d) -1.2 cm (e) None of these. A stationary block of mass m, lying on a horizontal frictionless surface, is attached to a horizontal spring. The block is pulled 10 cm to the right (+ direction) and released. You start your stop watch as the block passes through its equilibrium position for the first time. 2. If the mass of the block is increased by 4 times, is the final frequency of oscillation (a) T initial /4 (b) T initial /2 (c) 4 T initial (d) 2 T initial (e) Unchanged

The pendulum on the right has a frequency of 0.5 Hz. 1. What is its period? (a) 0.5 s (b) 1.0 s (c) 2.0 s (d) can’t tell 2. The ball is released from rest at the position 2 o shown above at t = 0 s. Its subsequent position is given by (a) 2 o sin( T t) (b) 2 o cos( T t) (c) sin( T t) (d) cos( T t) (e) - 2 o sin( T t) (f) - 2 o cos( T t) 3. Over the 5 s after the ball is released, how many radians does the argument of the cosine go through? (a) 2 B (b) 2.5 B (c) 5 B (d) 10 B (e) can’t tell

The block is pulled to the right some distance from the equilibrium position and released from rest. The surfaces are frictionless. Take displacement to the right as positive. Which of the following curves best represents the (i) position, (ii) velocity and (ii) acceleration of the block as a function of time? a) b) c) d) e) None of these