(Solved): 1. The graph of displacement versus time for a small mass m at the end of a spring is shown in Fig ...

1. The graph of displacement versus time for a small mass $$m$$ at the end of a spring is shown in Fig. At $$t=0,x=0.43m$$. a. If $$m=10$$ grams, find the spring constant, $$k$$. b. Write the equation for displacement $$x$$ as a function of time. 2. The position of a SHO as a function of time is given by $$x(t)=4.0\mathrm{cm}\cos \left(\frac{3?t}{4}+\frac{?}{6}\right)$$ where $$t$$ is in seconds and $$x$$ in meters. a. the period and frequency b. the position and velocity at $$\mathrm{t}=0$$ c. the velocity and acceleration at $$t=2.5\mathrm{s}$$. 3. An object with mass $$2.7\mathrm{kg}$$ is executing simple harmonic motion, attached to a spring with spring constant $$\mathrm{k}=310\mathrm{N}/\mathrm{m}$$. When the object is $$0.025\mathrm{m}$$ from its equilibrium position, it is moving with a speed of $$0.50\mathrm{m}/\mathrm{s}$$. a. Calculate the amplitude of the motion. b. Calculate the maximum speed attained by the object.