Oscillator. consider a h1271 molecule (force constant 313.8 n m1, equilibrium bond length 161 pm) in its vibrational ground state. (a) plot the probability density function (in pm1) as a function of the bond length (in pm). (b) calculate the probability of finding the molecule with its bond length 157 pm or shorter. [you will need the error function, look it up. use a computer to evaluate it (e. g. wolfram alpha website)]

Aperson stands on a platform, initially at rest, that can rotate freely without friction. the moment of inertia of the person plus the platform is ip. the person holds a spinning bicycle wheel with its axis horizontal. the wheel has moment of inertia iw and angular velocity ωw. take the ωw direction counterclockwise when viewed from above. part a what will be the angular velocity ωp of the platform if the person moves the axis of the wheel so that it points vertically upward?